OPINION

SUTTON, Circuit Judge.

Fred Kratt challenges his conviction for three counts of engaging in monetary transactions in criminally derived property, see 18 U.S.C. § 1957, and an $85,954 restitution order. We affirm.

I.

In June 2001, Kratt re-financed his Cessna airplane by obtaining a $301,535 loan from Bancorp South based on fraudulent income tax returns that inflated his adjusted gross income for 1999 and 2000. The bank received a security interest in Kratt's Cessna as collateral. When Kratt fell behind on his payments, the bank foreclosed on the plane, selling it for $210,700 in October 2003. The sale left an $86,137 deficiency on the loan. On December 29, 2003, Kratt obtained an unsecured loan from Bancorp South for $86,137, which the bank applied to the first loan two days later. That brought the first loan to a zero balance and allowed Bancorp South to release its security interest in the Cessna.

Kratt did little better in paying off the second loan. He made six payments between March and August 2004, only one of which (for $1546) made any dent in the principal. Bancorp South charged off the second loan in August 2004, which had a final balance of $85,945. Kratt declared bankruptcy in 2005 and discharged his debts, transforming the final loan balance into a permanent loss for the bank.

A grand jury indicted Kratt on one count of bank fraud, see 18 U.S.C. § 1344, one count of making a false statement on a loan application, see id. § 1014, three counts of engaging in monetary transactions in criminally derived property, see id. § 1957, and two counts that have no bearing on this appeal. At trial, the Government showed that Bancorp South deposited the proceeds of the $301,535 initial loan into Kratt's account through two separate deposits: one for $274,712.48 and one for $25,287.52. A jury convicted Kratt on all seven counts. The district court imposed a 46-month sentence, and it ordered Kratt to pay Bancorp South $85,945 in restitution.

II. A.

Section 1957 criminalizes "knowingly engag[ing] . . . in a monetary transaction in criminally derived property of a value greater than $10,000" if the underlying criminal offense was one of over 250 enumerated offenses, including bank fraud and making false statements on a loan application. 18 U.S.C. § 1957(a); see also id. §§ 1956(c), 1957(f)(3). "[C]riminally derived property," the statute adds, "is any property constituting, or derived from, proceeds obtained from a criminal offense." Id. § 1957(f)(2) (emphasis added).

The question raised by Kratt's appeal is this: Does "proceeds" mean profits or gross receipts? Put another way, did the Government have to establish the gross receipts Kratt received from the fraudulently obtained loans ( viz., the full $301,535 amount of the loans and the resulting $274,712.48 and $25,287.52 deposits) or did it have to establish the profits Kratt received from the fraudulently obtained loans ( viz., the net profits from the loan and deposits)? If "proceeds" means profits, as Kratt argues, the Government has a sufficiency-of-the-evidence problem, because it never proved that the money Kratt deposited into, and withdrew from, his Bancorp South account represented the profits, as opposed to the gross receipts, of his bank fraud or false statements. If "proceeds" means gross receipts, as the Government argues, Kratt does not have a leg to stand on in challenging these convictions on sufficiency grounds.

At the time of trial, case law suggested that "proceeds" means gross receipts, because our precedent included gross receipts within the definition of proceeds under 18 U.S.C. § 1956, a companion statute to § 1957. See United States v. Prince, 214 F.3d 740, 747 (6th Cir. 2000); United States v. Haun, 90 F.3d 1096, 1101 (6th Cir. 1996). Since then, however, the Supreme Court has held that "proceeds" means profits in the context of an illegal-gambling operation under § 1956. See United States v. Santos, ___ U.S. ___, 128 S.Ct. 2020, 2025, 170 L.Ed.2d 912 (2008). In the aftermath of Santos, we must answer three questions: (1) Does "proceeds" have the same meaning under §§ 1956 and 1957, which both use "proceeds" in defining the elements of the offenses, see 18 U.S.C. §§ 1956(a)(1), 1957(f)(2); (2) what does the Court's 4-1-4 decision in Santos stand for; and (3) does that holding require us to reverse Kratt's conviction?

Does "proceeds" under § 1957(f)(2) have the same meaning as "proceeds" under § 1956(a)? Yes. Congress enacted §§ 1956 and 1957 at the same time as part of the Money Laundering Control Act of 1986 — in truth as all of the Act because the twin statutes amount to the entirety of the legislation. See Pub.L. No. 99-570, Title XIII, § 1352, 100 Stat. 3207-21. "[T]he normal rule of statutory construction" under these circumstances is "that identical words used in different parts of the same act are intended to have the same meaning." Gustafson v. Alloyd Co., 513 U.S. 561, 570, 115 S.Ct. 1061, 131 L.Ed.2d 1 (1995).

It makes particular sense to follow that custom here because the two statutes cover the same subject matter in a common way. See Barnhart v. Walton, 535 U.S. 212, 221, 122 S.Ct. 1265, 152 L.Ed.2d 330 (2002); Comm'r v. Lundy, 516 U.S. 235, 249-50, 116 S.Ct. 647, 133 L.Ed.2d 611 (1996). The statutes criminalize similar acts — monetary transactions in criminal proceeds — and simply do so from slightly different angles: Section 1956 criminalizes classic money laundering, while § 1957 criminalizes moving around at least $10,000 in criminal proceeds for any purpose through a financial institution. The statutes cover the same predicate offenses — more than 250 of them. See 18 U.S.C. §§ 1956(c)(7), 1957(f)(3). And whether we define "proceeds" to refer to profits or gross receipts, both statutes would remain coherent and would contain no redundant provisions. See Santos, 128 S.Ct. at 2025. Given these similarities, there is no reason to define "proceeds" differently from one provision to the next.

What does Santos hold? The defendant in Santos operated an illegal lottery in Indiana and was convicted of running an illegal gambling business and money laundering. Id. at 2022-23. Santos launched a successful collateral attack on his money-laundering convictions under 28 U.S.C. § 2255, arguing that "proceeds" in § 1956 means profits, not gross receipts, and that the Government had not proved that the transactions underlying his convictions involved the profits of his illegal gambling business. Id. at 2023. The Supreme Court's 4-1-4 decision lays out three different ways to interpret "proceeds."

Writing for a four-Justice plurality, Justice Scalia reasoned that "proceeds" always means profits under § 1956. Santos, 128 S.Ct. at 2025. Dictionary definitions of proceeds, the term's use throughout Title 18 and the statutory context of § 1956, he explained, all failed to resolve the matter, because each interpretation was as plausible as the other. Id. at 2024-25. The plurality therefore invoked the rule of lenity and adopted the more defendant-friendly definition: "[P]roceeds" means profits. Id. at 2025.

Applying the rule of lenity was particularly appropriate, the plurality added, because defining proceeds as gross receipts would create a "merger problem" for a number of predicate offenses under § 1956. "[N]early every violation of" a number of predicate offenses listed in § 1956(f)(3), it turns out, also violate "the money-laundering statute," and money laundering sometimes "radically increases" the statutory maximum sentence compared to the merged offense. Id. at 2026. In Santos itself, for example, operating an illegal lottery had a statutory maximum of five years, while a § 1956 conviction raised the statutory maximum to 20 years. See id. at 2027; 18 U.S.C. §§ 1955(a), 1956(a)(1).

Justice Alito, writing for four Justices in dissent, reached the opposite conclusion, noting that the primary definition of "proceeds" was gross receipts, that this interpretation made sense in the context of this and related statutes and that accordingly § 1956 always encompasses gross receipts. See Santos, 128 S.Ct. at 2037 (Alito, J., dissenting). In his view, the rule of lenity had no place in the analysis because the context in which "proceeds" appeared suggested that it referred to gross receipts. See id. at 2036-37, 2045. Acknowledging that his interpretation created a merger problem, he responded that the answer was not to alter the statutory meaning of "proceeds" but to resolve any such problems at sentencing or, if necessary, through amendments to the sentencing guidelines. See id. at 2044.

Justice Stevens, writing for himself, concurred in the judgment in favor of Santos, but he rejected the always-the-one or always-the-other approaches offered by his colleagues. As he saw it, the meaning of "proceeds" in § 1956 varies depending on the underlying predicate offense: While "proceeds" means profits if the laundered funds derived from operating an illegal lottery, it might mean gross receipts if the laundered funds derived from distributing cocaine. See id. at 2031-32 (Stevens, J., concurring in the judgment). Two factors drove Justice Stevens' assessment of how to apply the provision in various settings and his ultimate decision to apply a profits definition to Santos. One, defining "proceeds" as profits when the predicate offense is operating an illegal lottery created a "merger problem" that "radically increase[d] the sentence for that crime" and led to a "perverse result" that "Congress could not have intended." Id. at 2033. Two, nothing in the legislative history of § 1956 suggested that Congress was aware of this problem and yet still chose to treat "proceeds" as gross receipts when the laundered funds derive from operating an illegal lottery. Id. Under these circumstances, Justice Stevens concluded, the rule of lenity tipped the scale in favor of defining "proceeds" as profits when the predicate offense is operating an illegal lottery. See id. at 2033, 2034 n. 7.

Because no opinion in Santos attracted a majority of Justices, the "position taken by those [Justices] who concurred in the judgment[] on the narrowest grounds" represents its holding. Marks v. United States, 430 U.S. 188, 193, 97 S.Ct. 990, 51 L.Ed.2d 260 (1977). That is easier said than done. Sometimes it is possible to identify the concurring opinion that "is a logical subset" of the other opinion (or opinions). King v. Palmer, 950 F.2d 771, 781 (D.C. Cir. 1991) (en banc); see also Triplett Grille, Inc. v. City of Akron, 40 F.3d 129, 134 (6th Cir. 1994). And sometimes it is not, making Marks an exercise in chasing the wind. Compare Triplett Grille, 40 F.3d at 134-35, with Anker Energy Corp. v. Consolidation Coal Co., 177 F.3d 161, 170 (3d Cir. 1999). Imagine, for example, if Justice Stevens had held that proceeds always means gross receipts absent both factors he identifies. It would be no more appropriate to call that approach "a logical subset" of Justice Scalia's than to call Justice Scalia's approach "a logical subset" of Justice Stevens'.

Yet there is a coherent way to apply Marks here. Justice Stevens' approach provides a logical subset of Justice Scalia's approach — at least in terms of outcomes. "[P]roceeds" does not always mean profits, as Justice Scalia concluded; it means profits only when the § 1956 predicate offense creates a merger problem that leads to a radical increase in the statutory maximum sentence and only when nothing in the legislative history suggests that Congress intended such an increase. Whenever a predicate offense satisfies this narrow rule, the Justices in the plurality would hold "proceeds" means profits as well, because they would define "proceeds" as profits for every predicate offense.

Resisting this conclusion, the Government maintains that Santos stands only for the proposition that "proceeds" means profits when the predicate offense is operating an illegal lottery. Because the plurality and Justice Stevens cannot agree on whether "proceeds" has a single meaning under § 1956 or a meaning that varies across distinct predicate offenses and because the reasoning of the opinions is irreconcilable, the Government reasons, the two opinions taken together stand only for the outcome in Santos, nothing more. But fundamental disagreements about how to interpret a statute do not necessarily destroy a subset-superset relationship between the two opinions. Otherwise, Marks would stand for little, as it generally will be the case that the legal reasoning of the plurality opinion and the legal reasoning of the concurring opinion(s) will differ. That is often why Justices (and judges) write separately in the first place. No matter how strongly the plurality may disagree with Justice Stevens' interpretive approach, his holding, though not all of his dicta, "will necessarily produce results" they agree with. Triplett Grille, 40 F.3d at 134 (internal quotation marks omitted). This is not a case, by way of contrast, in which the plurality opinion turned on statutory interpretation and the concurring opinion turned on constitutional interpretation, see, e.g., Welsh v. United States, 398 U.S. 333, 90 S.Ct. 1792, 26 L.Ed.2d 308 (1970), a situation that generally would not be amenable to a Marks analysis.

That said, we must acknowledge two unsatisfying aspects of this approach. It will require us to define "proceeds" for over 250 predicate offenses, see 18 U.S.C. §§ 1956(c), 1957(f)(3), a regime that may generate a cottage industry of Santos litigation for years to come. And it will create a more severe notice/rule-of-lenity problem than the one that predated Santos. Even after accounting for Justice Scalia's and Justice Stevens' opinions, "proceeds" remains an ambiguous term, but it is now one that the lower courts will place in one camp or the other based on an offense-by-offense inquiry that even the most law-abiding, prescient and lawyerly citizen would find hard to predict. Oddly enough, then, the rule of lenity considerations that drove Santos have greater force today than they did before the Court decided Santos. Yet a straightforward application of Marks requires us to apply a defendant-unfriendly approach to Kratt, and that is what we have done.

One other word on applying Santos. In some settings, a merger problem may exist under § 1956 but not under § 1957. Operating an illegal lottery, for example, likely falls in this category because most illegal lottery transactions involve less than $10,000 and many illegal lottery operators want to avoid the increased IRS and FBI scrutiny that comes with over-$10,000 monetary transactions through financial institutions. See 31 U.S.C. §§ 5313, 5324; 31 C.F.R. §§ 103.18, 103.22. Likewise, a conviction under § 1956, but not under § 1957, may lead to a radical increase in the statutory maximum. Because "proceeds" has the same meaning under both §§ 1956 and 1957, we must consider whether contrary legislative history, a merger problem or a radical increase in the statutory maximum exists under either §§ 1956 or 1957 when applying Santos. If the Santos rule applies under either statute, then "proceeds" means profits for both statutes.

If "proceeds" has the same meaning in §§ 1956 and 1957 and if Santos reversed a § 1956 conviction, does that require us to vacate Kratt's § 1957 convictions? No. In this case, it is clear, a merger issue arises because nearly every consummated bank fraud and false statement offense involves depositing, withdrawing, transferring or exchanging funds derived from the offense. See 18 U.S.C. § 1957. But it is not the kind of merger that troubled Justice Stevens. Neither a § 1956 nor a § 1957 conviction radically increases the statutory maximum sentence when the predicate offense is bank fraud or making false statements. Far from it: Sections 1956 and 1957 impose lower statutory maximums than bank fraud and false-statement offenses. See 18 U.S.C. § 1956(a)(1) (20 years); id. § 1957(b)(1) (10 years); id. § 1344 (30 years); id. § 1014 (30 years). Because Kratt's § 1957 conviction does not subject him to a markedly increased statutory maximum, there is no reason to consider whether the legislative history shows that Congress contemplated, and intended, any such outcome.

Santos thus does not require us to apply a profits definition of "proceeds" to Kratt's offenses. That leaves us with our prior precedents in this area, which apply a gross-receipts definition, see Prince, 214 F.3d at 748; Haun, 90 F.3d at 1101, and which support this conviction. Kratt does not contest that the two deposits and one withdrawal from his Bancorp South account involved the gross receipts of his bank fraud and false statement offenses. Accordingly, sufficient evidence supports Kratt's conviction on three counts of engaging in monetary transactions in criminally derived property.

That leaves an alternative ground for decision raised by the Government — a variation on which the concurrence embraces. In the last paragraph of its brief addressing these § 1957 convictions, the Government says the following, quoted in full:

The United States would further submit that even if Santos were applicable to the instant case, the transactions involved in counts 4, 5 and 6 of indictment 05-20368, that is, count 4 being a check for $20,000.00, the deposit mentioned in count 4 of $25,287.52, and the deposit in count 6 of $274,712.48 were in fact the net proceeds of the sum loaned which was received by the defendant as a result of his fraudulent activity. The fact that the defendant may have had greater liabilities than these loans, is irrelevant, as these liabilities do not pertain to any sentence inquired as a result of his fraudulent application for the loans. To extend the holding in Santos further than that, would to be put any court in the impossible position of proving a defendant's total financial picture to determine whether a specific criminal activity increased the defendant's solvency in matters unrelated to the activity.

Appellee Br. at 18-19.

If we understand the Government correctly, it is arguing that, "even if Santos" required us to adopt a "profits" definition of "proceeds," it still would win. In other words, under any interpretation of "profits," these transactions exceeded the $10,000 statutory minimum set forth in § 1957. The first answer to this argument is that the predicate for reaching it does not exist: We have held that proceeds means gross revenues, not profits, so there is no basis for reaching the Government's alternative theory of affirmance.

The second answer is that the Government did nothing to prove to the jury that the deposits and withdrawal represented the profits of Kratt's crimes and of course the jury was never instructed on the point. We cannot relieve the Government of its burden of proof on an essential element of a crime whenever we believe it might satisfy it. Cf. United States v. Gaudin, 515 U.S. 506, 510, 514-15, 115 S.Ct. 2310, 132 L.Ed.2d 444 (1995).

The third answer is that the definition of profits is far from self-evident. We can envision at least four definitions of profits in this setting: (1) the gross receipts of the fraudulently obtained loan; (2) the gross receipts of the loan minus the value of the security interest at the time of the loan; (3) the gross receipts of the loan minus the principal repaid and the amount recovered from liquidating the collateral or (4) the gross receipts of the loan minus the non-profit-generating uses of the loan proceeds, such as debt repayment. We agree with the concurrence that the last definition is unlikely. But no authority excludes the second definition, and under that definition Kratt obtained no profit from the loan. He received a $301,535 loan but gave the bank a $301,535 security interest in a Cessna valued at $350,000.

We also agree with the concurrence that "[t]he more prudent course" is invariably "to wait to consider . . . issues in a case where they are properly raised by the parties." Concurrence at 2 n. 1. But, with respect, that is what we have done. At Kratt's trial, the parties and district court assumed (based on existing Sixth Circuit law) that "proceeds" means gross revenues. On appeal, both parties squarely debated — that indeed is all they squarely debated — whether Santos changes Sixth Circuit law. Kratt said it did; the Government said it did not; and we refereed the dispute, holding that Santos does not change Sixth Circuit law in a way that benefits Kratt. The parties, by contrast, never debated the meaning of "profits," Kratt never offered a definition of the term and the Government's apparent alternative argument never mentions (or purports) to define "profits." In short, the issue we have decided — the effect of Santos on Sixth Circuit law — was the one question properly presented by the parties with respect to the § 1957 convictions.

B.

Kratt separately challenges the district court's $85,945 restitution order, see 18 U.S.C. § 3663A, claiming it exceeds Bancorp South's losses from the bank fraud and false statements. A "victim of the offense," the statute says, is "a person directly and proximately harmed as a result of the commission of" the offense, id. § 3663A(a)(2), and the Government must prove the bank's loss by a preponderance of the evidence, see id. § 3664(e); United States v. White, 492 F.3d 380, 418 (6th Cir. 2007). In calculating restitution, "the loss caused by the conduct underlying the offense of conviction establishes the outer limits of a restitution order." Hughey v. United States, 495 U.S. 411, 420, 110 S.Ct. 1.979, 109 L.Ed.2d 408 (1990); see also United States v. Sosebee, 419 F.3d 451, 459 (6th Cir. 2005).

In this instance, Bancorp South's $85,945 loss stemmed directly and proximately from Kratt's bank fraud and false statements. Had Bancorp South charged off the deficiency balance on the first loan, they would have suffered a loss of $86,137 due to the fraud. But instead the bank tried to mitigate the loss by rolling the deficiency balance into a new loan so Kratt could continue paying the balance down, a required course of action because the bank needed to get the first loan off its books so it could release its security interest in the foreclosed and resold Cessna. When this mitigation strategy failed seven months later, Kratt still owed $85,945 on the second loan. Because Bancorp South's sole motivation for issuing the second loan was to mitigate its losses on the first loan (and to release the security interest in the Cessna), the $85,945 amount arose directly and proximately from Kratt's fraudulent conduct.

Noting that the first loan was paid in full (on paper anyway) and that no fraud occurred in connection with the second loan, Kratt maintains that the second loan represents unrelated conduct that severs any link between the $85,945 loss and the bank fraud and false statements. Yet Kratt offers no evidence showing, or even hinting, that Bancorp South would have approved the second loan but for its losses on the first one. And the record contains several pieces of evidence, including uncontradicted testimony, supporting the Government's allegations: The second loan was for the exact amount of the outstanding balance on the first loan; it was issued by the same bank that issued the first loan two months after it sold the collateral underlying the first loan due to default; and the bank applied the proceeds to the first loan within two days of origination. This evidence amply satisfies the Government's preponderance burden.

III.

For these reasons, we affirm.