OPINION OF THE COURT

BECKER, Chief Judge.

This is an appeal by defendant Robert U. Syme, who owned and operated a number of individually incorporated ambulance companies which, according to the 31-count superseding indictment, fraudulently sought over-reimbursement through the Medicare and Medicaid programs. Syme was convicted on several counts of wire fraud, mail fraud, and False Claims Act violations, and on one count of making a false statement relating to a health care matter. Syme's corporate co-defendants were convicted on all counts and are not involved in this appeal. Each of the fraud and False Claims Act counts alleged that Syme engaged in two or more of the following forms of fraud when he billed the government for ambulance trips: (1) falsely identifying a Pennsylvania address for his companies and seeking reimbursement at the rate paid to Pennsylvania companies, when the claim should have been billed at the (lower) Delaware or Maryland rates; (2) falsely representing that ambulance transport was medically necessary; (3) providing false information about the destination of the ambulance trip; and (4) providing false information about the type of treatment that the patient being transported was going to receive.

Syme raises several challenges to his convictions. The principal challenge is that the indictment alleged and the District Court instructed the jury on a theory of fraud that is invalid as a matter of law. More particularly, Syme contends that the government's theory that he committed fraud by misrepresenting that Pennsylvania was the "home station" of his ambulance companies, thereby getting reimbursed at the Pennsylvania rate, is invalid as a matter of law because the term "home station" had not been authoritatively defined during the time covered in the indictment. We conclude, however, that this fraud theory is not legally invalid, but rather, at most, may have been unsupported by the evidence presented at trial. Because each challenged count also rests on a fraud theory that Syme does not challenge on appeal, we must affirm the convictions that Syme challenges on this basis. See Griffin v. United States, 502 U.S. 46, 57-58, 112 S.Ct. 466, 116 L.Ed.2d 371 (1991).

We will, however, vacate and remand for a new trial Syme's False Claims Act conviction on count 25 of the superseding indictment. Albeit quite inadvertently, the District Court committed plain error with respect to that count, constructively amending the indictment by instructing the jury on a fraud theory that was not alleged in the count. In noticing plain error in this case, we hold that constructive amendments, which are per se reversible under harmless error review, are presumptively prejudicial under plain error review. Because we find that the government failed to present sufficient evidence during the first trial for the jury to convict on the "medical necessity" theory on Count 25, the "medical necessity" theory must be removed from the scope of the new trial thereon. To retry count 25 based on that theory would violate the Double Jeopardy Clause.

Syme also attacks all counts of conviction on the grounds that the District Court erred in the admission of certain evidence. Primarily, he challenges the admissibility of the testimony of a physician expert witness on the grounds that it could not "assist the trier of fact to understand the evidence or to determine a fact in issue." Fed.R. Ev. 702. We disagree, concluding that his testimony that an ambulance trip is actually medically necessary is an issue on which the average juror could benefit from a physician's expert testimony. We reject Syme's other evidentiary objections summarily. See infra note 2.

Turning from the convictions to the sentence, we agree with Syme that the sentence imposed by the District Court needs be vacated because the District Court committed plain error in violation of the Ex Post Facto Clause by applying the Sentencing Guidelines' enhancement for fraud committed by "sophisticated means," which was not included in the Guidelines until after Syme committed the offenses in this case. We will remand for resentencing on this count. We reject, however, Syme's claim that the restitution order that the District Court imposed on him violates Apprendi v. New Jersey, 530 U.S. 466, 120 S.Ct. 2348, 147 L.Ed.2d 435 (2000). This claim presents a question of first impression in this Circuit, which we resolve by concluding that, because the statute under which the District Court sentenced Syme to pay restitution contains no maximum penalty, Apprendi does not apply.

I. Facts and Procedural History

From 1987 through late 1996, Syme owned and operated an ambulance company called Medical Services Corps, Inc. ("MSC"), which had its main office first in Stanton, Delaware, and after 1995, in Wilmington, Delaware. Syme created three corporate subsidiaries to MSC. In 1989, he founded NCC Transportation, Inc. ("NCC") and Elk Transportation, Inc. ("Elk"). In 1992 he created Independence EMS, Inc. ("Independence"). All three subsidiaries operated from MSC's Delaware offices and engaged in the business of providing ambulance transportation services. Ambulances from Syme's companies sometimes also operated in Pennsylvania, New Jersey, and Maryland. Syme exercised day-to-day control over MSC and all of its subsidiaries, including oversight of the ambulance dispatch and billing operations. One of the mainstays of Syme's ambulance businesses was transporting patients to and from regularly scheduled medical treatments. For example, his companies had contracts with the Delaware State Hospital to transport patients to the hospital for treatment.

The majority of the patients that Syme's companies transported were covered either by Medicare, the federally funded program that funds medical services for the elderly, or by Medicaid, a similar program that funds services for low-income people. The Health Care Financing Administration ("HCFA"), a federal agency within the Department of Health and Human Services ("HHS"), is responsible for coordinating and financing the reimbursement of health care service providers under the Medicare and Medicaid programs. During the period relevant to this case, HCFA contracted first with Pennsylvania Blue Shield and later with its subsidiary, Xact Medicare Services ("Xact"), to administer the reimbursement of Medicare claims. Xact was responsible for claims arising in Pennsylvania, New Jersey, and Delaware, and processed the claims for Medicare reimbursement submitted by Syme's ambulance companies.

Xact developed operational guidelines governing which claims would be reimbursed under Medicare consistent with HCFA policy memoranda. In order to get paid for transporting Medicare patients, ambulance companies were required to submit standard reimbursement requests to Xact with information about the patient, the purpose of the trip, and the starting point and destination. Xact would determine whether to reimburse an ambulance service for a trip depending on whether the trip met certain criteria. First, the ambulance trip had to be "medically necessary" as defined by Xact's guidelines. Second, the patient had to be transported for a treatment covered by Medicare's ambulance reimbursement guidelines. Third, the ambulance trip had to be to a covered destination. Certain destinations, such as hospitals, were covered by Xact's reimbursement program, while others, such as dental offices, were not.

Ambulance services were also required to record on their reimbursement forms a provider number that indicated the state in which their service was located. Most importantly, the rate of reimbursement that Medicare paid varied widely according to which state provider number the ambulance service used. The reimbursement rates for Pennsylvania ambulance services, for example, were almost twice as high as the rates for Delaware services.

Syme and his companies have long had a rocky relationship with HCFA and its subcontractors. In February 1982, Xact's predecessor, Pennsylvania Blue Shield, became concerned that Delaware Medical Services, Inc. ("DMS"), a separate company that Syme had formed around the same time as MSC, was filing duplicate claims for the same ambulance trip and billing at the higher Pennsylvania rate rather than at the Delaware rate. According to an affidavit by an employee in the HHS Office of the Inspector General, representatives from Pennsylvania Blue Shield spoke with Syme "in an attempt to educate [him] in the appropriate claim filing policies and procedures." Syme represented in this meeting that "he was inadequately reimbursed for ambulance service in Delaware."

In 1987, the government filed a civil suit against Syme and DMS, alleging, among other things, that DMS had falsely filed claims for Delaware ambulance trips using a Pennsylvania provider number in order to get reimbursed at the higher Pennsylvania rate. Syme settled the suit for $4,000 in May 1992, but did not admit any wrongdoing.

In April 1992, Donald Baxter, a Pennsylvania Blue Shield investigator, started looking into the location of MSC's three subsidiary companies. He visited the locations in Philadelphia that Syme had listed as the addresses for his three companies in the applications that he had submitted for Medicare provider numbers. At 4700 Cedar Avenue, the address listed on NCC's provider number application, Baxter found neither a garage, nor ambulances, but rather an apartment building. He also attempted to visit 3255 A Street, the address listed on Elk's provider number application, but found that the address did not exist. Finally, Baxter visited 3300 Fairmount Avenue, the address listed on Independence's application. At that address, he found a number of garages that appeared to be vacant.

Baxter then contacted Syme to ask him where his companies' ambulances were located. Syme told him that two ambulances were housed at 3300 Fairmount Avenue at the time, but that no ambulances were housed at 3255 A Street. In a follow-up letter to Baxter, Syme wrote that Elk and NCC had moved from 3225 A Street to 3300 Fairmount Avenue about one year earlier, and that all of the administrative offices and dispatching operations for all three of the subsidiaries had been moved to Stanton, Delaware. On April 13, 1992, after receiving the letter from Syme, Baxter returned to 3300 Fairmount Avenue. He visited the site twice, once at 12:30 a.m., and again from 4:25 p.m. until approximately 4:45 p.m., but saw no activity either time. Before leaving the site, Baxter taped the garage doors so that he could tell if anyone opened them while he was away. When he returned three days later, the tape had not been disturbed.

Baxter returned to 3300 Fairmount Avenue in July 1994 along with Klaus Placke, an investigator from Xact, and found that the garages and attached office space appeared to be empty. Following their visit to 3300 Fairmount Avenue, the investigators went to see Syme at his office in Stanton, Delaware. They asked him where the ambulances for NCC and Elk were located, and he replied that they were still housed at 3300 Fairmount Avenue. When the investigators told him that they had just been to the location and that it had looked empty, Syme replied that he had moved most of his operation to Delaware, but that he still housed one of NCC's ambulances at the Fairmount Avenue location. He added that NCC's one Philadelphia-based ambulance was then in Delaware for servicing and he showed it to the investigators. The investigators asked Syme why the supposedly Philadelphia-based ambulance had Maryland tags and a Maryland certification sticker, but he could not explain the discrepancy.

During the same visit, the investigators asked to see NCC and Elk's state licenses to operate ambulance services in Pennsylvania. Syme was unable to find the licenses, but asked the investigators to return the next day so that he could give them copies. When the investigators returned the next day, Syme told them that he had been mistaken, and that NCC and Elk were not licensed in Pennsylvania and consequently had no ambulances housed in Philadelphia. He said that Independence was licensed in Pennsylvania and operated one ambulance out of 3300 Fairmount Avenue. Following the visit, Placke, the Xact investigator, changed NCC and Elk's provider numbers to indicate that the two companies were Delaware providers that could be reimbursed only at the Delaware rate. He left Independence's provider number unchanged, and Independence continued to bill at the Pennsylvania rate.

The Pennsylvania state ambulance licensing authority was also investigating Syme's Philadelphia operations during the early- to mid-1990s. Independence originally received an ambulance license from Pennsylvania in 1992. In September 1993, however, Michael Tunney of the Philadelphia region of Pennsylvania's ambulance licensing authority, prompted by a call from his supervisor at the state licensing board, inspected Syme's purported 3300 Fairmount Avenue location. Tunney saw no employees and no activity at the location. He knocked on a door located next to the garages, but received no response.

Tunney also received applications signed by Syme for Pennsylvania ambulance licenses for NCC and Elk in September 1993. Each application listed 3300 Fairmount Avenue as a location out of which the company operated. Because he had visited the Philadelphia address only a few weeks earlier and found no activity, Tunney called Syme to inquire about the location that he had listed. Syme told him that there was not much activity at 3300 Fairmount Avenue. Tunney did not process the applications for NCC and Elk because, following his conversation with Syme, he had "a question in [his] mind about the veracity of the information in the application . . . as to whether or not [Syme] was really operating in Philadelphia."

Tunney visited the 3300 Fairmount Avenue location again soon after February 1995, after receiving Independence's application for relicensing, which Pennsylvania requires ambulance companies to submit every three years. He found that the building located at that address appeared to be empty and received no response when he knocked. Tunney therefore denied Independence's application for relicensing.

On March 10, 1998, a grand jury in the District of Delaware returned a 30-count indictment against Syme and his corporations, MSC, NCC, Elk, and Independence. The grand jury later returned a 31-count superseding indictment against the same defendants for offenses that allegedly occurred between October 1993 and March 1997. Our references hereafter are to the superseding indictment. Syme was charged in all counts of the indictment. Counts 1-4 allege mail fraud in violation of 18 U.S.C. § 1341. The indictment alleges that for each count in this group, Syme engaged in a "scheme to defraud" the HCFA in at least two of the following ways: (1) by falsely identifying a Pennsylvania address for his companies and fraudulently seeking reimbursement at the higher Pennsylvania rate when the claims should have been billed at the Delaware or Maryland rates (the "Pennsylvania rate theory"); (2) by falsely representing that ambulance transport was medically necessary (the "medical necessity theory"); (3) by providing false information about the destination of the ambulance trip (the "destination theory"); and (4) by providing false information about the type of treatment that the patient being transported was receiving (the "treatment theory").

Counts 1-4 allege that Syme's scheme to defraud caused the HCFA to send him checks through the U.S. Mail on four separate occasions to reimburse his companies for the ambulance trips in question. Counts 5-9 allege wire fraud in violation of 18 U.S.C. § 1343, pleading that Syme's companies electronically transmitted reimbursement requests to Pennsylvania Blue Shield that Syme knew contained false information. In each count, the indictment alleges two or more of the four theories of fraud described above.

Counts 10-29 allege violations of the False Claims Act, 18 U.S.C. § 287. The indictment divides these counts into three groups. Counts 10-12 apply to the Medicare payments that the defendants are alleged to have received fraudulently. Counts 13-17 apply to the reimbursement and copayments from Medicaid that the defendants are alleged to have fraudulently received. Counts 10-17 rely on all four theories of fraud: the Pennsylvania rate theory, the medical necessity theory, the destination theory, and the treatment theory. Counts 18-29 allege that Syme and his companies violated the False Claims Act by submitting duplicate bills for the same ambulance trip. In addition to the duplicate billing theory, each count in the 18-29 group also alleges one or more of the four fraud theories described above.

Count 30 alleges that Syme obstructed justice in violation of 18 U.S.C. § 1505 by failing to respond properly to a subpoena duces tecum issued by the Office of the Inspector General of the Department of Health and Human Services. Count 31 alleges that Syme made a false statement relating to a health care matter in violation of 18 U.S.C. § 1035 when he prepared a letter concerning the application for a provider number by Lifestar Ambulance Services, the renamed company that he had sold to one of the former managers of MSC, in which he falsely stated that "Mr. Robert Syme has no role whatsoever in Lifestar," when in fact he remained active in managing the company.

Following a seven-day trial, a jury convicted Syme on all of the mail and wire fraud counts (1-9), many of the False Claims Act counts (10-17, 19, 21, 23-25, 27, and 29), and the false statement count (31). Syme was acquitted on several of the False Claims Act counts (18, 20, 22, 26, and 28) and on the obstruction of justice count (30). The corporate defendants were convicted on all counts. After the trial, all defendants moved for a new trial and for judgment of acquittal, which the District Court denied in a published opinion. See United States v. Med. Servs. Corps, Inc., 43 F.Supp.2d 499 (D.Del. 1999). The Court sentenced Syme to a prison term of 37 months on each of the counts for which he was convicted, to be served concurrently, followed by three years of supervised release. In addition, the Court ordered Syme to pay special assessments totaling $1,750.00, and restitution to the HCFA of $100,000 (a $300,000 restitution order less a credit of $200,000). Following his sentencing, Syme filed a timely appeal. Because the most difficult issue that Syme raises on appeal is the validity of the Pennsylvania rate theory, we begin our discussion with that issue. However, we will first dispose of Syme's claims of improper admission of trial evidence in the margin.

II. Validity of the Pennsylvania Rate Theory A. The Parties' Contentions

The superseding indictment alleges that Syme and his companies fraudulently overcharged Medicare and Medicaid by submitting false bills that stated that the "home stations" of the ambulance companies were located in Philadelphia rather than in Delaware or Maryland, thereby getting reimbursed at the higher Pennsylvania rate. The indictment states that:

At all times material to this indictment, Medicare authorized reimbursement for ambulance services at pre-established rates based upon the home station of the ambulance. If an ambulance's home station was in Philadelphia, Pennsylvania, the ambulance company would be reimbursed at the rate for that part of Pennsylvania. If the ambulance's home station was in Delaware, the ambulance company would be reimbursed at the Delaware rate, which was lower than the rate for Philadelphia, Pennsylvania.

The indictment then goes on to allege that Syme and all of his companies:

submit[ted] bills to Medicare for ambulance services under a provider number which would be reimbursed at a Pennsylvania rate (which was substantially higher than the Maryland or Delaware rates) although the home station for the ambulances were [sic] either in Delaware or Maryland. Such bills should have been submitted under a Delaware or Maryland provider number, not under a Pennsylvania provider number.

The District Court also used the term "home station" in its jury instructions. The Court instructed the jury that in order to convict on the mail or wire fraud counts, it had to find that the defendants "knowingly submitted each claim for reimbursement at a higher Pennsylvania rate, although the ambulances' home station was in Delaware."

Syme bases his current challenge on the use of the term "home station." He contends that defects in the government's use of the term render the Pennsylvania rate theory both legally invalid and insufficiently supported by the evidence presented at trial. Syme submits three arguments attacking the legal validity of the Pennsylvania rate theory based on the use of the term "home station." First, he contends that neither the HCFA nor Xact had established a clear definition of the term "home station" during the period at issue in this case. Second, he asserts that even if "home station" had been defined, there was no official determination that an ambulance's "home station" would be the governing standard for determining reimbursement rates. Third, Syme argues that the application forms supplied by Xact, which he submitted in order to get Pennsylvania provider numbers for his ambulance companies, never asked for the companies' "home stations," but rather asked for their addresses. Syme contends that he therefore cannot be convicted of a scheme to defraud based on the fact that he misrepresented his companies' "home stations," because he never made any representations about their "home stations" at all.

Finally, Syme asserts that for the same reasons that he claims the Pennsylvania rate theory of fraud is legally invalid, the evidence presented at trial is also insufficient factually to support his conviction based on the Pennsylvania rate theory. In addressing these arguments, we must of course first define our standard of review, which we set forth in the margin.

We agree with Syme that the evidence presented at trial shows little beyond the fact that there was a general understanding in the ambulance community of the definition of the term "home station." The earliest document that the prosecution presented that defines "home station" in the reimbursement context is a February 2, 1995 letter from Xact to an ambulance provider that defines a transporting vehicle's "home station" as its "point of departure." Testimony presented at trial also shows that there was a debate within the ambulance community during the time relevant to this case as to whether "home station" was the correct reimbursement standard.

Syme is also correct that none of the forms that he completed in order to get Pennsylvania provider numbers asked for the "home stations" of his ambulance companies. However, two of the provider number applications asked for both an "address" and a "mailing address;" another form asked for both a "physical location" and a "mailing address." Syme supplied Philadelphia addresses as the "address" and "physical location" as well as the "mailing addresses" on these forms.

The government counters that "home station" was sufficiently defined and understood to be the governing reimbursement standard during the time relevant to the case. Alternatively, the government argues that Syme's behavior would constitute fraud under any of the meanings of "home station" or alternative reimbursement standards that may have been debated during the relevant period. The government also contends that it demonstrated a pattern of deception that is sufficient to demonstrate Syme's intent to defraud Medicare and Medicaid.

B. Griffin and Yates

As we noted above, the prosecution has presented alternative theories of guilt to support each count in the indictment. Each count rests on two or more of the four main theories that the government presented: the Pennsylvania rate theory, the medical necessity theory, the destination theory, and the treatment theory. See supra at 139. When a criminal defendant appeals a conviction in which the prosecution presented more than one theory of guilt and the jury returned a general verdict, we apply the holding of Griffin v. United States, 502 U.S. 46, 112 S.Ct. 466, 116 L.Ed.2d 371 (1991). Griffin restated the longstanding rule that if the evidence is insufficient to support a conviction on one alternative theory in a count but sufficient to convict on another alternative theory that was charged to the jury in the same count, then a reviewing court should assume that the jury convicted on the factually sufficient theory and should let the jury verdict stand. Id. at 49-50, 112 S.Ct. 466. However, under Griffin, if one of two or more alternative theories supporting a count of conviction is either (1) unconstitutional, or (2) legally invalid, then the reviewing court should vacate the jury verdict and remand for a new trial without the invalid or unconstitutional theory. Id. at 56, 112 S.Ct. 466 (citing Stromberg v. California, 283 U.S. 359, 367-68, 51 S.Ct. 532, 75 L.Ed. 1117 (1931) (reversing a conviction where one of the alternative guilt theories was unconstitutional), and Yates v. United States, 354 U.S. 298, 312, 77 S.Ct. 1064, 1 L.Ed.2d 1356 (1957) (reversing a conviction where one of the possible grounds was legally invalid because it was time-barred)).

The rationale for this distinction is that a jury is presumed to be able to distinguish factually sufficient evidence from factually insufficient evidence. That function is central to its role as fact finder. The jury is not presumed, however, to be able to distinguish accurate statements of law from inaccurate statements. Id. at 59, 112 S.Ct. 466; Tenner v. Gilmore, 184 F.3d 608, 611 (7th Cir. 1999). And Griffin made it clear that claims regarding the insufficiency of evidence do not fall into the categories of a legally invalid or an unconstitutional basis for conviction. The Court explained:

In one sense "legal error" includes inadequacy of evidence — namely, when the phrase is used as a term of art to designate those mistakes that it is the business of judges (in jury cases) and of appellate courts to identify and correct. In this sense "legal error" occurs when a jury, properly instructed as to the law, convicts on the basis of evidence that no reasonable person could regard as sufficient. But in another sense — a more natural and less artful sense — the term "legal error" means a mistake about the law, as opposed to a mistake concerning the weight or the factual import of the evidence. . . . [W]e are using "legal error" in the latter sense.

502 U.S. at 58-59, 112 S.Ct. 466. The question of which side of Griffin's line the present challenge to the Pennsylvania rate theory falls — whether it is a claim about the sufficiency of the evidence presented on this theory, or (as Syme contends) an argument that the theory is legally invalid (he does not argue that it is unconstitutional) — is dispositive of Syme's challenge to the theory as a basis for conviction. If we find that the Pennsylvania rate theory was, at most, unsupported by the facts presented at trial, then we will let the challenged counts of conviction stand, because each one rests on at least one other fraud theory that Syme does not challenge. If we find that the Pennsylvania rate theory, as it was alleged in the indictment and charged to the jury, constituted an error of law, then we must reverse Syme's conviction on the counts in which the theory was alleged and remand these counts for a new trial.

A theory upon which a criminal charge rests is legally invalid under Griffin if the indictment or the district court's jury instructions are based on an erroneous interpretation of law or contain a mistaken description of the law. This "invalid legal theory" exception to the longstanding rule that general verdicts will stand even if one of the possible grounds for conviction was unsupported by the evidence, comes from Griffin's attempt to rationalize Yates v. United States, 354 U.S. 298, 77 S.Ct. 1064, 1 L.Ed.2d 1356 (1957), with the bulk of the Court's precedents. Prior to Yates, the only exception that the Court had applied to the rule of presuming that general verdicts rest on permissible grounds was that, when "any of the [grounds] in question [was] invalid under the Federal Constitution, the conviction cannot be upheld." Stromberg, 283 U.S. at 368, 51 S.Ct. 532. The Court applied this exception in many cases involving "general-verdict convictions that may have rested on an unconstitutional ground." Griffin, 502 U.S. at 55, 112 S.Ct. 466 (listing cases). In Yates, the Court extended the exception to cover grounds that were not unconstitutional, but rather were legally invalid. Yates held that the statute of limitations had already run on the charge that the defendants had "cause[d] to be organized units of the [Communist] Party." 354 U.S. at 302, 77 S.Ct. 1064. This "organizing" offense was one of two theories that were the basis for a conspiracy charge. Id. The question whether the statute of limitations had run turned on the meaning of the statutory term "to organize." Id. at 303-304, 77 S.Ct. 1064. The lower courts had construed the term "to organize" to "connote a continuing process which goes on throughout the life of an organization," but the Supreme Court rejected this definition, finding that "to organize" meant "to enter into the creation of a new organization" Id. at 310, 77 S.Ct. 1064.

Because the Supreme Court held that the term "organize" referred to the initial establishment of the Communist Party, and it was undisputed that the three-year statute of limitations had run between the time the Communist Party was initially organized and when the defendants were indicted, it held that the "organizing" charge was time-barred. Because it was "impossible to tell which ground the jury selected," either the "organizing" charge, or the alternative charge, the Court set aside the jury verdict and remanded for a new trial. Id. at 312, 77 S.Ct. 1064. It did so, however, based on a finding that the lower courts had erred on a purely legal question, i.e., the construction of a statutory term.

There does not appear to have been any dispute in Yates over the factual issue of when the Communist Party was initially organized. It was not as if the prosecution in that case simply failed to present sufficient evidence that the establishment of the Communist Party took place within three years prior to the indictment. If that were the case, then the jury would have been capable of determining that the facts were insufficient to show that the statute of limitations had not run and the Court would have presumed that the jury rested its general verdict on one of the factually supported grounds. However, because the lower court misinterpreted the meaning of the statutory term "to organize," erroneously permitting the "organizing" charge to go to the jury, the jury was faced with a potential ground for conviction that was based on an invalid interpretation of the statute. Because the jury is not assumed to be able to distinguish between correct and incorrect legal interpretations, the Yates Court reversed the jury's general-verdict conviction.

Griffin, in addition to referencing a claim that was time barred as an example of a legally inadequate ground for conviction, also cited the example of a theory of conviction that "fails to come within the statutory definition of a crime." 502 U.S. at 59, 112 S.Ct. 466. Again, this situation presents a strictly legal question — the interpretation of whether the scope of a statutory definition of a crime extends to acts alleged in an indictment.

C. Analysis

In the present case, neither the indictment nor the District Court's instructions to the jury relied on erroneous interpretations of the law or contained mistaken descriptions of the relevant legal standards regarding the Pennsylvania rate theory of fraud as an element of Syme's fraud and False Claims Act charges. The indictment alleges that Syme's misrepresentation of his companies' home stations was a "scheme to defraud" within the meaning of the mail and wire fraud statutes, and a "false or fraudulent claim" under the False Claims Act, and the prosecution undertook to demonstrate the existence of that scheme and Syme's specific intent to engage in the scheme. See supra note 3 (listing the elements of mail and wire fraud and False Claim Act violations). Concomitantly, the District Court instructed the jury that in order to convict Syme for mail or wire fraud, the prosecution had to demonstrate that Syme "knowingly submitted each claim for reimbursement at a higher Pennsylvania rate, although the ambulances' home station was in Delaware."

The "home station" theory of fraud on which the District Court instructed the jury certainly falls within the scope of the fraud statutes and the False Claims Act. To prove the existence of this scheme and Syme's intent to engage in the scheme, the government needed to demonstrate that a definition of the term "home station" existed and that Syme was aware of the meaning of "home station" when he submitted his claims for reimbursement from Medicare and Medicaid using a Pennsylvania provider number. But even if there was no HCFA regulation or written instruction from Xact on the definition of "home station," and no clear indication that "home station" was the appropriate standard for reimbursement, the prosecution could still have demonstrated that Syme knew that this was the standard that Xact wanted ambulance companies to apply and that he knowingly used a Pennsylvania provider number in order to get paid at a higher rate.

The meaning of the term "home station" and Syme's intent with respect to falsifying the "home station" of his ambulance companies was an issue on which both sides focused at trial. The government presented witnesses to attempt to show both (1) that "home station" had a generally recognized meaning during the times relevant to this case; and (2) that Syme understood the meaning of the term "home station." For example, the prosecution presented testimony from Jill Shaffer, a policy coordinator from Xact, that from 1990-95 "the home station requirement was that [Xact] reimbursed an ambulance company based on where [its] ambulance vehicles were garaged or housed." On cross examination, however, Shaffer admitted that the definition that she provided for "home station" came from a section of the Medicare manual defining "carrier jurisdiction," which referred to the insurance company with jurisdiction over processing a claim.

Similarly, government witness Patrick Kennedy, the founder of the Ambulance Association of Pennsylvania, also testified that there was an understanding in the ambulance industry that "home station" meant "where your major business center would be," i.e., "where your major offices are . . . where your billing center is . . . [and][m]ost importantly, where your communication center is." However, on cross-examination, Kennedy admitted that during the times relevant to this case, there was no written definition of "home station" as it relates to reimbursement rates. Prosecution witnesses also testified that Syme knew of the different rates paid to Pennsylvania and Delaware providers and had complained that they were unfair, and that Xact officials had met with Syme to instruct him on the proper practices for submitting reimbursement claims. Thus, the questions whether "home station" had a meaning, and whether Syme knew that meaning, were highly disputed issues of fact in this trial, and were presented to the jury as such.

Because the District Court correctly instructed the jury that it must find that Syme knowingly engaged in a scheme to defraud (in the case of the fraud counts) or made a false claim (in the case of the false claims counts), and because the jury was presented with conflicting testimony about whether the term "home station" had a meaning that Syme was aware of, we presume under Griffin that the jury focused on and was able to decide this disputed factual issue. There was a factual dispute regarding the term "home station," which the jury was competent to resolve. Under Griffin, we will presume that the jury did resolve this factual dispute, and that it relied on the Pennsylvania rate theory only if it found that the government presented sufficient evidence that the term "home station" had a meaning that Syme knew.

We conclude that, while the government simply may have failed to present sufficient evidence on the definition of the term "home station" to make out the elements of the fraud and False Claims Act charges, neither the indictment nor the District Court's instructions contained a "mistake about the law" regarding the Pennsylvania rate theory that, under Griffin, would require reversing the counts in question. 502 U.S. at 59, 112 S.Ct. 466. Whether the government succeeded in presenting sufficient evidence so that a jury could have convicted Syme beyond a reasonable doubt is a question we need not reach, because even assuming that the evidence presented was insufficient to convict Syme on the Pennsylvania rate theory, Griffin instructs that we should presume that the jury relied on an alternative theory of guilt within the same count that is both legally valid and supported by sufficient evidence. Because Syme leaves unchallenged at least one of the fraud theories charged in each fraud and False Claims Act count for which he was convicted, we must uphold the jury verdict on each of these counts.

Because we will not remand these counts for a new trial (except for count 25, which we will remand because the District Court constructively amended it, see infra Part III), we need not reach Syme's challenges to the factual sufficiency of the medical necessity, destination, and treatment theories of fraud, which he challenges for some of the counts for which he was convicted. If we were to vacate and remand any other counts for a new trial, then we would need to evaluate each challenged theory of guilt to determine whether the evidence presented at the first trial was sufficient. If we found that it was not sufficient, then we would be required to remove that theory from the scope of the new trial. See Burks v. United States, 437 U.S. 1, 17-18, 98 S.Ct. 2141, 57 L.Ed.2d 1 (1978); see also infra Section III.D. However, because Syme leaves unchallenged at least one alternative theory of guilt on each count of conviction, we must affirm those counts and need not evaluate the evidentiary sufficiency on the alternative theories of guilt that Syme does challenge. We address below Syme's challenge to the evidentiary sufficiency of the "medical necessity" theory in count 25. See infra Section III.D.

III. Constructive Amendment to Counts 18-29

Syme contends that the District Court erred by instructing the jury on the Pennsylvania rate theory of fraud for counts 18-29, even though the indictment does not allege the theory in those counts. Syme did not raise this argument in the District Court and we therefore apply the plain error standard of review. See Fed.R.Crim.P. 52(b); see also supra note 4.

A. Did the District Court Err by Constructively Amending the Indictment?

A constructive amendment occurs where a defendant is deprived of his "substantial right to be tried only on charges presented in an indictment returned by a grand jury." United States v. Miller, 471 U.S. 130, 140, 105 S.Ct. 1811, 85 L.Ed.2d 99 (1985) (quoting Stirone v. United States, 361 U.S. 212, 217, 80 S.Ct. 270, 4 L.Ed.2d 252 (1960)) (internal quotation marks omitted). A constructive amendment to the indictment constitutes "a per se violation of the fifth amendment's grand jury clause." United States v. Castro, 776 F.2d 1118, 1121-22 (3d Cir. 1985).

In their text, counts 18-29 of the superseding indictment charge Syme under three alternative theories of fraud: (1) that he submitted Medicare forms indicating that ambulance trips were medically necessary when they were not ("medical necessity"); (2) that he falsified the description of the treatment, service, or destination of the ambulance trip ("treatment, service, or destination"); and (3) that he submitted duplicate bills for single ambulance trips, one using a Delaware ambulance provider number, and one using a Pennsylvania ambulance provider number ("duplicate billing"). The text of the indictment for counts 18-29 does not specifically charge Syme under the Pennsylvania rate theory of fraud. However, a chart accompanying these counts, which lists the various theories supporting each charge, does list the Pennsylvania rate theory in the sections for counts 19, 21, 23, 24, 27, and 29. The chart appeared in the superseding indictment as follows:

Although the Pennsylvania rate theory was neither mentioned in the text of the indictment, nor listed in the accompanying chart for several of the counts in the 18-29 group, the District Court instructed the jury that it could convict on all of the counts in this group based on the Pennsylvania rate theory. In its jury instructions, the Court stated:

The next criminal act that has been charged is false claims. Counts 10 through 29 of the indictment charge that the defendants did make and present and caused to be made and presented to the Health Care Financing Administration, . . . claims for services provided to Medicare and/or Medicaid patients, the defendants knowing the claims to be false and fraudulent, which is prohibited by federal law.

The indictment charges that defendants falsely submitted bills that were not medically necessary and were not for covered services, and that bills were improperly submitted at the higher Pennsylvania rate.

(emphasis added). The District Court repeated its erroneous instruction on the Pennsylvania rate theory in its response to the following question from the deliberating jury (which references the abbreviations for the government's different theories of fraud in the case, explained in the margin):

First let me read the question. The question says: "Must we find all elements of the false statement proven?" Then, there is parentheses, "(i.e., PA, MN, treat., dest.)," close parens, "to render a verdict on each count, or would only one element suffice?"

The first part of my answer is this: In your deliberations, to render a verdict on the false statement counts, you must find that the government has proven beyond a reasonable doubt each element of the crime of making a false statement. And in the instructions I provided you, I gave you the law of what the elements are for the crime of false statement.

. . . .

Now, in the question, the second part of my answer is, when you refer to items such as "PA," "MN," "Treat." and "Dest." as elements, I interpret your question to mean entries on the statements. In order to find on an entry, you would only have to find one of the entries was proven to be false beyond a reasonable doubt, as long as all the other elements were proven to your satisfaction beyond a reasonable doubt.

So I answer you in two parts. Using the word "element," all elements of the crime have to be proven beyond a reasonable doubt. One of the elements is there has to be a false entry. It only has to be proven beyond a reasonable doubt that one of the entries entered meets all of the elements.

The government concedes that the District Court "committed error in its instructions to the jury on Counts 18, 20, 22, 25, 26 and 28" because the sections of the indictment corresponding to these counts do not reference the Pennsylvania rate theory. As to the remaining counts in the 18-29 group, the government argues that the District Court did not constructively amend the indictment because the Pennsylvania rate theory was alleged in the indictment for these counts. The government relies on the chart that was included in the indictment. See supra at 149. The chart lists the various charges, and the theories on which each is based. Each horizontal row of the chart represents a different count of the indictment. Each vertical column in the chart has a heading telling which information corresponds to which count (e.g., "Billing Date" or "Money Billed"). One heading labeled "False State." refers to the category of statement or statements that the count alleges Syme to have falsely made on his reimbursement forms. This box contains abbreviations that correspond with the different categories of information that the government charged Syme with falsifying.

The abbreviation "PA" appears in the "False State." column for the rows corresponding to counts 19, 21, 23, 24, 27, and 29. As we explained above, see supra note 6, "PA" is defined earlier in the indictment to mean "submit[ting] bills . . . for transportation services billed at the Pennsylvania rate instead of the Delaware or Maryland rate." Therefore, argues the government, Syme was effectively indicted in these counts on the Pennsylvania rate theory and the District Court therefore did not amend these counts in its jury instructions or its answer to the jury's question. Syme responds that including the term "PA" in the chart corresponding to the counts in question was alone insufficient when the theory was not also described in the text of the indictment that corresponded to these counts. It is particularly confusing, argues Syme, because when "the same `PA' abbreviation was used in a chart pertaining to the other fraud and false claims counts, it was used together with charging language."

Although the indictment is below the level of clarity to which prosecutors should aspire, we agree with the government that the chart sufficiently alleges the Pennsylvania rate theory for counts 19, 21, 23, 24, 27, and 29 for the purpose of determining whether there has been a constructive amendment to the indictment. There is nothing impermissible about setting out allegations in an indictment by a chart as long as the terms used in the chart are clearly defined, as they were here. Cf. United States v. Heath, 122 F.3d 682, 684 (8th Cir. 1997) (holding that it was not error for a sentencing court to "consider all of the acts charged in the indictment" including a chart that was "incorporated by reference" in one of the counts). Indeed, Federal Rule of Evidence 1006 recommends the value of presenting evidence to a jury in the form of a chart when doing so would increase the clarity of presentation. In sum, while the use of charts in this indictment is somewhat inconsistent internally, we find that the chart accompanying counts 19, 21, 23, 24, 27, and 29 makes it sufficiently clear that those counts alleged the Pennsylvania rate theory. Therefore, we find that the District Court erred by constructively amending the indictment only as to counts 18, 20, 22, 25, 26 and 28.

B. Was the Error Clear or Obvious?

The government concedes that the District Court's error was clear with respect to counts 18, 20, 22, 25, 26, and 28. Cases from the Supreme Court and this court hold that it violates the Grand Jury Clause of the Fifth Amendment when a court instructs a jury on a ground for conviction that is not fully contained in the indictment. See Miller, 471 U.S. at 140, 105 S.Ct. 1811; Castro, 776 F.2d at 1121-22. Nowhere in counts 18, 20, 22, 25, 26, or 28, including the chart, does the indictment allege the Pennsylvania rate theory. Therefore, we agree that it was clear error for the District Court to instruct the jury on the Pennsylvania rate theory for those counts.

C. Did the Error Affect Syme's Substantial Rights?

Under plain error review, a defendant must also show that the clear error "`affected [the defendant's] substantial rights.'" United States v. Nappi, 243 F.3d 758, 762 (3d Cir. 2001) (quoting United States v. Olano, 507 U.S. 725, 734, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993)). "In most cases, the language about affecting substantial rights `means that the error must have been prejudicial,' that is, `[i]t must have affected the outcome of the district court proceedings.'" United States v. Stevens, 223 F.3d 239, 242 (3d Cir. 2000) (quoting Olano, 507 U.S. at 734, 113 S.Ct. 1770). Syme was found not guilty on counts 18, 20, 22, 26, and 28. Therefore, the constructive amendment of these counts obviously did not affect his substantial rights. That leaves only the question whether the constructive amendment of count 25 affected Syme's substantial rights.

Syme does not attempt to demonstrate that the constructive amendment to count 25 was prejudicial. Instead, he submits that our holding in United States v. Castro, 776 F.2d 1118, 1121-22 (3d Cir. 1985), that a constructive amendment is per se reversible error, compels us to find that a constructive amendment per se affects a defendant's substantial rights under plain error analysis. The government argues the opposite, maintaining that under plain error review, it is the defendant's burden to show that the constructive amendment was prejudicial. Neither Castro nor United States v. Somers, 496 F.2d 723 (3d Cir. 1974), the Third Circuit case on which Castro relies for the proposition that a constructive amendment is per se reversible, specify whether the per se rule that they cite applies under both harmless error and plain error review. Stirone v. United States, 361 U.S. 212, 80 S.Ct. 270, 4 L.Ed.2d 252 (1960), the U.S. Supreme Court opinion that both Castro and Somers cite as authority to support the per se rule, reviewed a constructive amendment to which the defendant raised an objection in the district court, and thus does not necessarily extend the per se rule to the plain error context. See id. at 214, 80 S.Ct. 270.

However, even if the general statements from Castro and Somers must be read to extend to the plain error context, it is uncertain whether this application of the per se rule has survived Olano, which recognized broader discretion for appellate courts exercising plain error review. See United States v. Dipentino, 242 F.3d 1090, 1095 (9th Cir. 2001) (noting that it is uncertain whether the Ninth Circuit's per se reversal rule for constructive amendments under plain error review has survived Olano, but declining to decide). Several courts of appeals have considered the question whether a constructive amendment is per se reversible under the plain error standard, but the circuits are divided and the resulting law is checkered, as explained in the margin. However, the question whether the per se reversal rule of Castro and Somers applies in the context of plain error review appears to be one of first impression for us.

As noted above, Olano stated that in order for an error to "affect substantial rights" under the plain error test, the defendant usually must show that the error was "prejudicial," that is that it "affected the outcome of the district court proceedings." 507 U.S. at 734, 113 S.Ct. 1770. However, as we recently recognized in United States v. Adams, 252 F.3d 276 (3d Cir. 2001), "the Supreme Court has cautioned that some errors to which no objection was made should be `presumed prejudicial' if the defendant cannot make a specific showing of prejudice." Id. at 285 (quoting Olano, 507 U.S. at 735, 113 S.Ct. 1770). We also noted that under Olano, "there may be a special category of forfeited errors that can be corrected `regardless of their effect on the outcome,'" and stated our assumption that this category is coextensive with the category of "structural" constitutional errors. Id. at 285 n. 6 (quoting Olano, 507 U.S. at 735, 113 S.Ct. 1770). We concluded that " Olano dictates that when a defendant fails to object[,] . . . his claim on appeal is reviewed for plain error — which requires the defendant to make a specific showing of prejudice, unless he can show that the error should be presumed prejudicial, or that the error belongs in a special category of errors that should be corrected regardless of prejudice (i.e., the category of structural errors)." Id. at 285.

Adams addressed a denial of the right of allocution (i.e., the right of a criminal defendant to make a statement prior to sentencing). Adams did not reach the issue whether the denial of the right of allocution constituted structural error; rather it held that it fell into the other category of errors that should be presumed prejudicial. The question in this case, therefore, is whether constructive amendments fall into either of the two exceptions to the general rule that a defendant must demonstrate prejudice under plain error review.

We turn first to the question whether constructive amendments fall into Olano's category of "those errors that should be presumed prejudicial if the defendant cannot make a specific showing of prejudice." Olano, 507 U.S. at 735, 113 S.Ct. 1770. In Adams, we found that the denial of a defendant's constitutional right of allocution falls within Olano's category of "errors that should be presumed prejudicial" in the plain error context. 252 F.3d at 287 (quoting Olano, 507 U.S. at 735, 113 S.Ct. 1770) (internal quotation marks omitted). We noted that "[g]iven the nature of the right[of allocution] and the difficulty of proving prejudice from its violation, we conclude that we should presume prejudice when a defendant shows a violation of the right and the opportunity for such a violation to have played a role in the district court's sentencing decision." Id. at 287.

Like a denial of the right of allocution, a constructive amendment also violates a basic right of criminal defendants, the grand jury guarantee of the Fifth Amendment. We follow the holding of Adams that some serious errors should be presumed prejudicial in the plain error context even if they do not constitute structural errors and find that constructive amendments fall into that category. Similar to the plight of a defendant who is denied the right of allocution, it is very difficult for a defendant to prove prejudice resulting from most constructive amendments to an indictment. In the present case, for example, it is nearly impossible for Syme to demonstrate that he was convicted on count 25 based on the Pennsylvania rate theory, rather than on one of the other theories of guilt pleaded in that count (i.e., that the constructive amendment altered the outcome on that count), even though there is a substantial possibility that he was convicted based on the Pennsylvania rate theory. As Syme points out, the District Court identified the Pennsylvania rate theory as the "crux" of the government's case. Therefore, we will apply in the plain error context a rebuttable presumption that constructive amendments are prejudicial (and thus that they satisfy the third prong of plain error review).

Applying the rule that constructive amendments are presumptively prejudicial under plain error review to the present case, we must determine whether the government has effectively rebutted the presumption that the constructive amendment was prejudicial. The government argues that the pattern of counts on which the jury convicted Syme reveals that it did not rely on the District Court's erroneous instructions, and that Syme was therefore not prejudiced by the constructive amendment. The jury convicted Syme on all of the counts in the 18-29 range in which the Pennsylvania rate theory was alleged in the chart accompanying the indictment but found him not guilty on all but one of the counts in which the Pennsylvania rate theory was not alleged. This pattern holds for all of the counts in this range except for count 25, in which the Pennsylvania rate theory was not alleged, but on which the jury convicted Syme. Thus, the government contends that the jury actually relied on the chart accompanying the indictment rather than the District Court's instructions and that Syme therefore could not have been prejudiced by the erroneous jury instructions.

We find this argument unconvincing. We do not believe that the "pattern of convictions" is sufficient to support the conclusion that the government urges us to draw about the jury's motivations, i.e., that it relied on the chart and ignored the Court's instructions. As a rule, we presume the opposite — that the jury follows a district court's instructions. See, e.g., Jermyn v. Horn, 266 F.3d 257, 312 (3d Cir. 2001). We therefore conclude that the government has not rebutted the presumption that the constructive amendment was prejudicial.

Applying a presumption of prejudice to our plain error review of this constructive amendment, we conclude that the constructive amendment to count 25 affected Syme's substantial rights. Leaving this error uncorrected would seriously affect the fairness and integrity of the proceeding. See Olano, 507 U.S. at 736, 113 S.Ct. 1770. We will therefore exercise our discretion to vacate Syme's conviction on count 25 of the superseding indictment and remand for a new trial on that count.

D. Was the Evidence Presented Sufficient for the Jury to Convict Syme Based on the "Medical Necessity" Theory of Fraud for Count 25?

Syme challenges the "medical necessity" theory of fraud in several of the fraud and False Claims Act counts for which he was convicted. As we explained above, we need not reach the question whether the evidence was sufficient to support the "medical necessity" theory on all of the counts in which it was alleged because each count contained an alternative theory of fraud that Syme does not challenge on this appeal. Therefore, under the rule from Griffin v. United States, 502 U.S. 46, 112 S.Ct. 466, 116 L.Ed.2d 371 (1991), we affirm the convictions, assuming that they rested on the factually supported ground. However, because we reverse count 25 and remand for a new trial thereon, we must consider Syme's challenge to the factual sufficiency of the "medical necessity" theory of fraud pleaded in that count.

Citing Burks v. United States, 437 U.S. 1, 98 S.Ct. 2141, 57 L.Ed.2d 1 (1978), Syme contends that if we find that there was not sufficient evidence presented at trial to support the medical necessity theory as it applies to count 25, we must exclude it from the new trial that we order on this count. Syme's trial counsel moved to dismiss the case for insufficient evidence at the close of the government's case, thus preserving the issue for appeal. We will review Syme's challenge to the sufficiency of the evidence to support the "medical necessity" theory of fraud in count 25 under the harmless error standard. See Fed R.Crim. P. 52(a).

When the sufficiency of the evidence to support a jury's verdict is challenged, "we must view the evidence in the light most favorable to the government and must sustain the jury's verdict if a reasonable jury believing the government's evidence could find beyond a reasonable doubt that the government proved all the elements of the offense." United States v. Pressler, 256 F.3d 144, 149 (3d Cir. 2001) (quoting United States v. Rosario, 118 F.3d 160, 163 (3d Cir. 1997)) (internal quotation marks and alterations omitted). In fact, "only when the record contains no evidence, regardless of how it is weighted, from which the jury could find guilt beyond a reasonable doubt, may an appellate court overturn the verdict." United States v. Anderson, 108 F.3d 478, 481 (3d Cir. 1997) (quoting United States v. McNeill, 887 F.2d 448, 450 (3d Cir. 1989)) (internal quotation marks and alterations omitted).

Count 25 refers to an August 3, 1994 ambulance trip in which NCC transported 80-year-old patient Ruth Graham. Dr. Leaser, the government's expert medical witness, testified that, based on his review of Graham's medical files, it was his opinion that it was not necessary to transport Graham by ambulance. Leaser based his opinion that ambulance transport was not necessary for Graham largely on notes made by the medical personnel at the nursing home where Graham lived, which indicated that she was ambulatory and could sit up unassisted. He cited a record that stated that as of January 1994, Graham was able to ambulate without assistance. He also noted that Graham's records indicated that in late March 1994, she was able to sit up without assistance and participate in an occupational therapy session.

But the government asked Leaser only if he had reviewed "the medical records for Graham for [the] dates of service January 20th, 1994 and March 17th, 1994." Leaser did not mention consulting any medical evidence recorded after March 1994, and his testimony suggests that he did not review Graham's medical files for dates after March 1994. Leaser noted that, in addition to Graham's medical records near the January 20, 1994 and March 17, 1994 ambulance trips, he "also looked at one other date . . . [on which] there was an ambulance transport . . . 2/16/94." (emphasis added). However, Graham's health could have deteriorated during the more than four months that passed between the date of the last medical record upon which Leaser relied and the August 3, 1994 ambulance trip in question. Therefore, although we "view the evidence and the inferences logically deducible therefrom in the light most favorable to the government," McNeill, 887 F.2d at 450, we conclude that due to the government's failure to put forth any evidence more current than March 1994, no reasonable jury could find beyond a reasonable doubt that Graham's August 3, 1994 ambulance trip was not medically necessary.

Because we conclude that the government presented insufficient evidence for a reasonable jury to have convicted Syme on count 25 based on the "medical necessity" theory in the first trial, we must address the question whether to allow the government to retry that theory on remand, or to limit the remand exclusively to the "treatment" theory (which Syme does not challenge). Syme argues that Burks instructs this court not to allow the government to retry a theory on which the government presented insufficient evidence the first time around. In Burks, the Supreme Court considered whether the Double Jeopardy Clause of the U.S. Constitution bars an appellate court that reverses a conviction for insufficiency of the evidence presented at trial from remanding the count of conviction for a new trial. The court of appeals in Burks (1) found that at trial the "Government had failed to come forward with sufficient proof of petitioner's capacity to be responsible for criminal acts," (2) held that the district court should have entered a judgment of acquittal in the first instance, and (3) remanded the case for a new trial. 437 U.S. at 10-11, 98 S.Ct. 2141. The sole issue before the Supreme Court was whether it is proper for an appeals court to remand a case for a new trial after finding that the verdict was insufficiently supported by the evidence presented at trial.

The Court found that it is not proper, holding that the "Double Jeopardy Clause forbids a second trial for the purpose of affording the prosecution another opportunity to supply evidence which it failed to muster in the first proceeding." Id. at 11, 98 S.Ct. 2141. The Court has stated that this principle, which "prevents the State from honing its trial strategies and perfecting its evidence through successive attempts at conviction," lies "at the core of the Clause's protections." Tibbs v. Florida, 457 U.S. 31, 41, 102 S.Ct. 2211, 72 L.Ed.2d 652 (1982). While Burks held that it was improper to order retrial of a whole count that the evidence was insufficient to support, we see no reason why the Double Jeopardy Clause would not also bar retrial on an alternative theory of guilt that the evidence was insufficient to support in a single count of conviction. The government does not argue that this error was harmless. Therefore, we will restrict the scope of the new trial on count 25 to the "treatment" theory, excluding both the Pennsylvania rate theory (because it was not alleged in the indictment), and the "medical necessity" theory (because the government presented insufficient evidence to support it in the first trial).

IV. Upward Adjustment for "Sophisticated Means" under the Sentencing Guidelines

Syme argues that the District Court violated the Ex Post Facto Clause by applying a two-level sentence enhancement for the commission of fraud by "sophisticated means" pursuant to § 2F1.1(b)(5)(c) (1998) of the United States Sentencing Guidelines. Because Syme raises this objection for the first time on appeal, we review the claim under the plain error standard. See Fed.R.Crim.P. 52(b); see also supra note 4.

The "sophisticated means" enhancement did not become effective until November 1, 1998, more than a year after the last conduct charged in the indictment. We have held that "[a]s a general rule, sentencing courts must apply the guidelines in effect at the time of sentencing, not at the time of the crime," but that where, as here, "such retroactivity results in harsher penalties, Ex Post Facto Clause problems arise, and courts must apply the earlier version." United States v. Kopp, 951 F.2d 521, 526 (3d Cir. 1991); see also U.S.S.G. § 1b1.11(b) (2001) ("If the court determines that use of the Guidelines Manual in effect on the date that the defendant is sentenced would violate the ex post facto clause of the United States Constitution, the court shall use the Guidelines Manual in effect on the date that the offense of conviction was committed.").

The government concedes that the first two prongs of plain error review are met, i.e., that the District Court erred by applying the "sophisticated means" enhancement, and that this error was clear. The government challenges the third prong of the plain error standard, however, contending that Syme's substantial rights were not prejudiced by the error because the range of possible sentences under the correct sentencing level (level 19, which calls for a sentence of 30-37 months) overlaps with the range of sentences under the erroneous sentencing level (level 21, which yields a sentence of 37-46 months). However, in United States v. Knight, 266 F.3d 203 (3d Cir. 2001), we held that under plain error review, "an error in application of the Guidelines that results in use of a higher sentencing range should be presumed to affect the defendant's substantial rights." Id. at 207. As does this case, Knight addressed the situation where the erroneous sentencing range overlapped with the correct sentencing range. The government has failed to rebut this presumption of prejudice. We conclude that this error too "seriously affects the fairness, integrity, or public reputation of judicial proceedings" to be left uncorrected. United States v. Olano, 507 U.S. 725, 736, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993) (internal quotation marks and alternation omitted). Therefore, we will vacate Syme's sentence and remand to the District Court with instructions to sentence Syme without applying the "sophisticated means" enhancement.

V. Did the Restitution Order Violate Apprendi?

The District Court ordered Syme to pay $100,000 in restitution to the HCFA (a $300,000 restitution order less a $200,000 credit) pursuant to the Victim and Witness Protection Act (VWPA), 18 U.S.C. § 3663. Syme contends that the restitution order violates Apprendi v. New Jersey, 530 U.S. 466, 120 S.Ct. 2348, 147 L.Ed.2d 435 (2000). Syme failed to raise this objection in the District Court, and therefore we review for plain error. See Fed.R.Crim.P. 52(b); see also supra note 4.

The operative rule from Apprendi is as follows: "Other than the fact of prior conviction, any fact that increases the penalty for a crime beyond the prescribed statutory maximum must be submitted to a jury, and proved beyond a reasonable doubt." 530 U.S. at 490, 120 S.Ct. 2348. We consider restitution orders made pursuant to criminal convictions to be criminal penalties. United States v. Edwards, 162 F.3d 87, 91 (3d Cir. 1998) (holding that restitution ordered under the Mandatory Victims Restitution Act (MVRA), 18 U.S.C. § 3663A, constitutes punishment for the purpose of Ex Post Facto Clause analysis); United States v. Sleight, 808 F.2d 1012, 1020 (3d Cir. 1987) (finding that under the Federal Probation Act, restitution "remains inherently a criminal penalty"); United States v. Palma, 760 F.2d 475, 479 (3d Cir. 1985) (holding that a restitution ordered under the VWPA is a criminal penalty). We therefore hold that restitution ordered under 18 U.S.C. § 3663 constitutes "the penalty for a crime" within the meaning of Apprendi. The jury in this case was not charged with finding the amount of restitution owed to the HCFA. Therefore, the question is whether the District Court's restitution order increased beyond the statutory maximum the penalties that Syme faced. If so, the order violated Apprendi.

Section 3663(a)(1)(A) of the VWPA provides: "The court, when sentencing a defendant convicted of an offense under this title, . . . may order, in addition to or, in the case of misdemeanor, in lieu of any other penalty authorized by law, that the defendant make restitution to any victim of such offense. . . ." 18 U.S.C. § 3663(a)(1)(A) (emphasis added). The highlighted language specifically indicates that restitution orders are penalties that a district court may impose when sentencing a defendant for any offense under title 18. Restitution orders have long been treated as part of the sentence for the offense of conviction, and not, as Syme appears to contend, separate enhancements to the underlying offense. See, e.g., Sleight, 808 F.2d at 1020 (holding that "restitution . . . is imposed as a part of sentencing"); Palma, 760 F.2d at 479 (noting that the legislative history of the VWPA "amply demonstrates that Congress intended restitution to be an integral part of the sentencing process").

Therefore, because the language of section 3663 specifically applies that section to all offenses defined in title 18, and because it has been the traditional practice of district courts to include restitution as part of the sentence for the offense of conviction, we think that the appropriate place to look for the statutory maximum as that term applies in the Apprendi context, is the restitution statute itself. But section 3663 does not specify a maximum amount of restitution that a court may order. The statute provides guidelines that a sentencing judge may use to determine the amount of restitution, but does not prescribe a maximum amount. The Apprendi rule therefore does not apply to restitution orders made pursuant to 18 U.S.C. § 3663, because Apprendi applies only to criminal penalties that increase a defendant's sentence "beyond the prescribed statutory maximum." 530 U.S. at 490, 120 S.Ct. 2348.

VI. Conclusion

For the reasons stated above, we will vacate Syme's False Claims Act conviction on count 25 of the superseding indictment and remand that count for a new trial based only on the "treatment" theory of fraud. We will also vacate the sentence imposed by the District Court and remand for resentencing with instructions not to apply the "sophisticated means" enhancement of § 2F1.1(b)(5)(c) (1998) of the Sentencing Guidelines. In all other respects, we will affirm the judgment of the District Court.