MINER, Circuit Judge:

Appellants Robert J. Mallon, Robert J. Attanasio and Francis S. LaMagra challenge their judgments of conviction entered in the United States District Court for the Eastern District of New York (Mishler, J.), following a jury trial. They were jointly tried, along with three other defendants, for two conspiracies to impede the Internal Revenue Service ("IRS") in the ascertainment, computation, assessment and collection of income taxes and for various substantive counts, including submitting, and aiding and abetting the submission of, materially false income tax returns and obstructing justice. Because each appellant was charged with only one of the two conspiracies, each made a pretrial motion for severance. These motions were denied. Appellants here challenge those rulings, arguing, inter alia, that the conspiracies were separate and distinct. Robert Attanasio challenges, as well, the denial of his motion for severance made at the close of the government's case; he contends that co-defendant Valentino would provide exculpatory testimony only at a separate trial.

Additionally, LaMagra and Mallon contend that there was a constructive amendment of the indictment and that, as a result, the government did not prove the essential nature of the conspiracy with which they were charged. Appellants challenge also the "two-inference" jury charge given by the district court.

For the reasons detailed below, we affirm the judgments of conviction.

BACKGROUND

A. Facts

Six defendants were involved in the conspiracies charged in the indictment: Louis J. Attanasio (brother of appellant Robert Attanasio), Marie L. Attanasio (Louis' wife), Joseph Valentino, and the three appellants.

1. See-Clear Conspiracy

Valentino was the acting vice-president of the See-Clear Maintenance Corporation ("See-Clear"), which provided maintenance services at the U.S. Coast Guard facility on Governor's Island in New York Harbor. At Valentino's behest, both Louis and Robert Attanasio were placed on the See-Clear payroll. Louis and Robert claimed their wages as income on their tax returns, filed jointly with their respective spouses, for the years 1981-1983; they attached to the returns W-2 forms furnished by See-Clear.

There was evidence, however, that neither Louis nor Robert worked at See-Clear. For instance, Wilfred Allen, the shop steward for the union to which all See-Clear employees on the Island were required to belong, testified that he never heard of Louis or Robert Attanasio, and that he did not recognize them in the courtroom. Charles W. Smith, the president and owner of See-Clear, testified that he never had met Robert until they were arraigned together and that Louis did not work for See-Clear. He further testified that when he discovered Robert Attanasio's name on the payroll, Valentino told him Robert was a cleaner on Governor's Island and that Robert was not related to Louis Attanasio.

2. Capital Gains Conspiracy

This conspiracy involved two fraudulent transactions reported on the joint tax returns of Louis and Marie Attanasio ("Attanasios") filed for the years 1983-1984. The 1983 return indicated a long-term capital gain of $250,000 from a sale of C L Tool Company ("C L") stock, which, according to the return, had been acquired years earlier for $50,000. Similarly, the 1984 return showed a capital gain of $291,000 from a sale of "Injection Molds." The Attanasios reduced their tax liability substantially by treating these transactions as capital gains rather than as ordinary income. The transactions were in fact fabricated, as the following discussion will illustrate.

a. The C L Transaction

During the relevant period, Mallon practiced law in New Jersey and performed all the legal work for Donato Sardella, the owner of C L. Sardella testified that, in 1981, he transferred some of his stock in C L to an unknown woman named "Maria" [sic], who, Mallon told him, would take C L public. Sardella received no money for this transfer. When the proposed public offering did not materialize, Sardella signed, at the direction of Mallon, a stock repurchase agreement.

A paper trail was orchestrated by Mallon to create the impression that Sardella paid Louis and Marie Attanasio for the repurchase. Sardella testified that Mallon persuaded him to write checks to Mallon and to the "Robert J. Mallon, Esq. Trust Account" in return for cash. Mallon caused additional funds to be deposited into the trust account. For example, he deposited cash and checks that he had third-parties write to Sardella, which Sardella endorsed. (Sardella did not receive the proceeds of these checks, though he was paid $5,000 for his part, $1,000 of which he returned to Mallon.) LaMagra, a financial consultant purportedly involved in taking C L public, contributed approximately $100,000 to the trust account. Mallon subsequently withdrew the funds from the trust account by writing checks worth $300,000 to, or for the benefit of, Louis and Marie Attanasio. Subtracting the $50,000 that they allegedly paid for the C L stock in 1981, the Attanasios reported the proceeds from this spurious stock repurchase as the $250,000 capital gain on their 1983 tax return.

b. The Injection Mold Transaction

Mallon also performed legal services for Richard Niclaus, who was involved in the plastic molding business. At some time in 1984, Mallon asked Niclaus if he had any injection molds to sell. Niclaus replied that he had three "dead molds" — molds for which there was no commercial demand and worth only their weight as scrap, i.e., $100,000. Mallon thereafter presented Niclaus with three bills of sale indicating a sale of the molds from Marie Attanasio to Niclaus for $300,000. Niclaus testified that he did not pay this money, but rather received $2,000 cash.

In early 1984, approximately $304,000 was deposited to another Mallon trust account. Again, much of this amount originated from LaMagra. $300,000 of this escrow money then was issued by Mallon to Marie Attanasio. All these checks were deposited, negotiated or cashed by Marie and Louis Attanasio, who then reported these proceeds on their 1984 tax return as the $291,000 capital gain.

3. Preparation of the Tax Returns

LaMagra provided financial data regarding Louis Attanasio's See-Clear salary and the capital gains transactions to Jerrold Berr, who used the information to prepare Louis and Marie Attanasio's 1983 and 1984 tax returns. (Berr testified that he thought that he was preparing draft work-ups merely to help the Attanasios assess their tax liability.) LaMagra also signed the name of Paul S. Roden, Jr., an accountant who had suffered a disabling stroke early in 1983, as the preparer of the 1983 return, and his own name as the preparer of the 1984 return.

B. The Indictment

The "Introduction" of the indictment states that Louis Attanasio "received substantial income from loansharking and conducting an illegal gambling business." Count 1 of the indictment charges Louis Attanasio, Robert Attanasio and Valentino with the See-Clear conspiracy, i.e., conspiring to defraud the IRS by impairing the ascertainment, computation, assessment and collection of the income taxes owed by Louis and Robert Attanasio for the years 1981-1983, in violation of 18 U.S.C. § 371.

Count 2 charges Louis and Marie Attanasio and appellants Mallon and LaMagra with the capital gains conspiracy. The opening paragraph of this count alleges a conspiracy to defraud the IRS "by impairing, obstructing and defeating its lawful government function of the ascertainment, computation, assessment, and collection of the revenue, namely income taxes of LOUIS J. and MARIE L. ATTANASIO for the calendar years 1983 and 1984." A subheading, "Means of the Conspiracy," follows, and reads in part:

Among the manner and means by which the defendants would and did carry out the objects of the conspiracy and insure the success of their venture were the following:

(A) It was a part of the aforesaid conspiracy that the defendants sought to conceal a substantial source and amount of income of the defendants LOUIS J. ATTANASIO and MARIE L. ATTANASIO.

(B) It was a further part of the aforesaid conspiracy that, in order to provide the defendant LOUIS J. ATTANASIO and MARIE L. ATTANASIO with a claimed source of legitimate income to explain and support expenditures, the defendants created false capital gains transactions for the defendants LOUIS J. ATTANASIO and MARIE L. ATTANASIO for the years 1983 and 1984 and laundered approximately $600,000.00 through attorney trust accounts maintained in whole or in part by the defendant ROBERT J. MALLON.

Overt acts then are listed under a separate subheading, and the count closes by charging a violation of 18 U.S.C. §§ 371 3623. The remaining counts, Counts 3-10, consist of sundry substantive charges relating to the two conspiracies.

C. The District Court 1. Rulings

Prior to trial, each appellant moved for severance of the counts on the ground that they alleged two entirely distinct conspiracies. Mallon sought additionally to sever his trial from LaMagra's, contending that only then would LaMagra testify that the C L and injection-mold transactions were legitimate. During the government's case, LaMagra and Mallon objected to the introduction of tape recordings and testimony regarding Louis Attanasio's loansharking and gambling activities. Louis was the only one of the appellants whose voice was recorded on the tapes. LaMagra requested that the tapes be suppressed, or alternatively, that LaMagra's trial be severed or the trial bifurcated so that the jury could decide a verdict as to those defendants against whom the tapes were inadmissible, before receiving the tapes against the remaining defendants. At the close of the government's case, Robert Attanasio moved to sever his trial from that of Valentino, contending that only then would Valentino testify that Robert was Valentino's driver and that the See-Clear payroll listed him as a custodian because there was no provision on the payroll for a driver. All these pre-trial and trial motions were denied.

The prosecutor, during her opening statement and again during her summation, alleged that as part of the capital gains conspiracy, Mallon and LaMagra laundered Louis Attanasio's dirty money through the Mallon trust accounts. During rebuttal summation, however, the prosecutor argued that "the indictment does not charge money laundering" and that "the government doesn't have to prove where the money came from."

LaMagra moved for a judgment of acquittal of Count 2 at the close of the prosecution's case, noting that, contrary to the allegation of the indictment, there was no evidence that the money purportedly laundered through the trust account emanated from Louis or Marie Attanasio. The court denied this motion. LaMagra objected also to the prosecutor's argument on rebuttal summation that the money laundering need not be proved, and requested an instruction that the prosecution must prove the $600,000 originated with the Attanasios. The court overruled the objection and denied the request.

During its final instructions to the jury, the court gave the following charge requested by Robert Attanasio: "[I]f you find that the evidence respecting the defendant is as consistent with innocence as it is with guilt, then it is your duty to accept the inference which favors innocence. The reason for this is obvious: Since the inferences are in balance there is necessarily a reasonable doubt." No trial counsel objected to this portion of the charge.

2. Convictions and Sentences

Following jury verdicts, Mallon and LaMagra were convicted of the capital gains conspiracy charged in Count 2, a violation of 18 U.S.C. §§ 371 3623. Mallon was convicted also of two counts of aiding and abetting Louis and Marie Attanasio in the submission of materially false returns, in violation of 26 U.S.C. § 7206(1) and 18 U.S.C. § 2, and was acquitted of one count of obstruction of justice. Robert Attanasio was convicted of three counts of filing a materially false income tax return, in violation of 26 U.S.C. § 7206(1); he was acquitted, however, of the See-Clear conspiracy alleged in Count 1.

All three appellants were sentenced to terms of imprisonment of one year and one day. Robert Attanasio was sentenced also to a three-year term of probation and ordered to pay a $150 special assessment. Mallon was fined $7,500, plus a $150 special assessment. LaMagra was fined $10,000, plus a $50 special assessment. All are on bail pending appeal.

D. Contentions on Appeal

The appellants, having adopted each other's arguments pursuant to Federal Rule of Appellate Procedure 28(i), dispute the district court's rulings on severance and the loansharking tapes. They argue again that the conspiracies charged in Counts 1 and 2 are separate and distinct. They further contend that, at a separate trial, the loansharking tapes would not have been admissible against any of the defendants, including Louis Attanasio, and that, in any event, they were prejudiced by the "spillover effect" of these tapes.

LaMagra and Mallon urge, as well, that the government has not proved the "essential nature" of the conspiracy charged in Count 2 — that Louis and Marie Attanasio were the source of the money that the defendants sought to conceal by way of the false capital gains transactions. They argue that, by stating that the government need not prove the source of the money, the court improperly constructively amended Count 2 of the indictment.

Appellants contend also that the "two-inference" jury charge given by the district court was clear error requiring reversal because our Circuit previously has condemned such a charge.

DISCUSSION

A. Joinder

Rule 8(a) of the Federal Rules of Criminal Procedure governs the joinder of offenses, whereas Rule 8(b) governs the joinder of defendants. Where, as here, the joinder involves both multiple offenses and multiple defendants, Rule 8(b) must be applied. United States v. Turoff, 853 F.2d 1037, 1043 (2d Cir. 1988). The Rule requires an allegation that the defendants "have participated in the same act or transaction or in the same series of acts or transactions constituting an offense or offenses." Fed.R.Crim.P. 8(b). We read this to mean that the acts must be "unified by some substantial identity of facts or participants," or "arise out of a common plan or scheme," United States v. Porter, 821 F.2d 968, 972 (4th Cir. 1987), cert. denied, ___ U.S. ___, 108 S.Ct. 1108, 99 L.Ed.2d 269 (1988); see also United States v. Green, 561 F.2d 423, 426 (2d Cir. 1977), cert. denied, 434 U.S. 1018, 98 S.Ct. 739, 54 L.Ed.2d 764 (1978). Further, the propriety of Rule 8 joinder "is subject to full appellate review," Turoff, 853 F.2d at 1042, and where "joinder should not have been permitted, a conviction must be reversed, unless failure to sever was harmless error," id.; see also United States v. Lane, 474 U.S. 438, 445, 106 S.Ct. 725, 730, 88 L.Ed.2d 814 (1986).

Here, the two conspiracies are sufficiently related for joinder to withstand judicial scrutiny. The transactions alleged in both conspiracy counts were a part of a series of acts that shared a common purpose: to conceal and launder Louis Attanasio's income, including that which may have derived from loansharking. Furthermore, there was an overlap of participants and acts. Specifically, Louis Attanasio participated in both conspiracies; for each year, he reported proceeds from at least one of the two conspiracies, and in 1983 he reported income from both conspiracies. LaMagra provided, for the preparation of the 1983 return, information regarding both Louis Attanasio's See-Clear salary and the C L transaction. In the same fashion, LaMagra supplied information about the injection mold transaction for the preparation of Louis and Marie Attanasio's 1984 tax return. He also signed both returns, using the name of the accountant, Paul S. Roden, Jr., for the 1983 return. Any "reasonable person would easily recognize the common factual elements that permit joinder," Turoff, 853 F.2d at 1044.

The actions of Robert Attanasio and Mallon were intertwined with the See-Clear and the capital gains conspiracies, respectively. Because each of these appellants "participated in the same series of acts" as his co-conspirators, United States v. Bernstein, 533 F.2d 775, 789 (2d Cir.), cert. denied, 429 U.S. 998, 97 S.Ct. 523, 50 L.Ed.2d 608 (1976), the joinder of each with his co-conspirators was proper. See id.

Even if the joinder under Rule 8(b) were error, it is harmless "when evidence tending to prove the charge that should have been severed would nevertheless have been admissible at the trial of the objecting codefendant, and was admitted subject to appropriate limiting instructions." United States v. Turbide, 558 F.2d 1053, 1061 (2d Cir.), cert. denied, 434 U.S. 934, 98 S.Ct. 421, 54 L.Ed.2d 293 (1977). Despite Mallon's assertions to the contrary, the loansharking evidence was properly admitted as to each appellant, in that it demonstrated intent and motive in creating the fraudulent transactions. Moreover, the district judge considered the admission of this evidence under both Federal Rules of Evidence 403 (exclusion of relevant evidence on grounds of prejudice) and 404(b) (evidence of other crimes, wrongs, or acts admissible to show motive and intent) and gave appropriate limiting instructions to the jury.

Finally, Robert Attanasio's motion for severance, pursuant to Federal Rule of Criminal Procedure 14 (relief from prejudicial joinder), properly was denied. He waived this claim by waiting until the government rested its case. This is so even though he claims to have made the motion as soon as he discovered that Valentino, who previously had agreed to testify on his behalf, would not testify. Federal Rule of Criminal Procedure 12(b)(5) specifically requires defendants to raise before trial "[r]equests for a severance of charges or defendants under Rule 14."

B. Failure of Proof: Constructive Amendment of Count 2

Mallon and LaMagra claim that the government failed to prove the conspiracy charged in Count 2, because there was no evidence presented that Louis or Marie Attanasio was the source of the money laundered. Mallon and LaMagra characterize the laundering as essential to the nature of the charged conspiracy. In support of this theory, they note that subparagraphs (A) and (B) of the Means section — which allege that defendants "sought to conceal a substantial source and amount of income" of the Attanasios, "created false capital gains transactions" for the Attanasios and "laundered approximately $600,000.00 through attorney trust accounts" — describe the allegations therein as being " part of the aforesaid conspiracy" (emphasis added). They note also that the Introduction of the indictment refers to Louis Attanasio's supposed loansharking income.

We do not agree with appellants' characterization. Count 2 of the indictment charges the crime of conspiracy to defraud the IRS of income taxes owed by Louis and Marie Attanasio. The count does not charge money laundering. Because the references to money laundering lie within the "Means" portion of the indictment, the essential nature of the charged conspiracy is not affected by the laundering allegations. The allegations of money laundering add nothing but gloss to the alleged conspiracy, and they need not be proved, see United States v. Toney, 598 F.2d 1349, 1355-56 (5th Cir. 1979), cert. denied, 444 U.S. 1033, 100 S.Ct. 706, 62 L.Ed.2d 670 (1980).

Mallon and LaMagra assert that the opening paragraph of Count 2 cannot be isolated as the "charging" section because the paragraph does not mention the false capital gains transactions that are, even by the government's definition, essential to the conspiracy. Both the C L and injection mold transactions, however, are included in the "Overt Acts" section of the indictment. Clearly, the overt acts "effect the object of the conspiracy," United States v. Rosenblatt, 554 F.2d 36, 39 (2d Cir. 1977) (emphasis omitted) (quoting 18 U.S.C. § 371).

Mallon and LaMagra call attention to our caution in Rosenblatt that because "the punishment that may be imposed under § 371 . . . depends on whether the `object' of the conspiracy is a felony or a misdemeanor . . . [,] specificity with respect to the `object' of the conspiracy is essential." Id. at 39. We held there that an indictment that charged only "conspiracy to defraud the United States," without more, was insufficient to define the central nature of the conspiratorial plan, and thus was deficient. Id. at 41. In the present case, however, there is more. The object of the conspiracy is qualified in the indictment: The conspiracy is to defraud the IRS "by impairing, obstructing and defeating its lawful government function of the ascertainment, computation, assessment, and collection of the revenue, namely income taxes of LOUIS J. and MARIE L. ATTANASIO for the calendar years 1983 and 1984."

In Rosenblatt, we held also that "[t]he law of conspiracy requires agreement as to the `object' of the conspiracy," id. at 38, but it need not be shown that the conspirators have agreed on the "details" of their criminal enterprise; only the "essential nature of the plan" must be agreed upon. Id. (quoting Blumenthal v. United States, 332 U.S. 539, 557, 68 S.Ct. 248, 256, 92 L.Ed. 154 (1947)). Here, the evidence supports a finding that the defendants agreed to the essential nature of a single plan, that is, to defraud the IRS with regard to the Attanasio's taxes. Specifically, Mallon "had to know what kind of criminal conduct was in fact contemplated," id. at 39 (quoting United States v. Gallishaw, 428 F.2d 760, 763 n. 1 (2d Cir. 1970)), as he was instrumental in orchestrating the fabricated transactions. As for LaMagra, many of the checks deposited into the Mallon trust originated with him, and he provided the financial data for and signed the returns. Regardless of the origin of the funds, there was sufficient evidence for a jury to find that these appellants embraced the object of the conspiracy.

In a similar vein, Mallon and LaMagra urge that because the court did not require proof of money laundering, a constructive amendment of the indictment occurred, requiring reversal of the judgments of conviction. A constructive amendment of an indictment "occurs when `the terms of the indictment are in effect altered by the presentation of evidence and jury instructions which so modify essential elements of the offense charged that there is a substantial likelihood that the defendant may have been convicted of an offense other than that charged in the indictment.'" United States v. Mollica, 849 F.2d 723, 729 (2d Cir. 1988) (quoting United States v. Hathaway, 798 F.2d 902, 910 (6th Cir. 1986)). In contrast, a "variance" of an indictment "occurs when the charging terms of the indictment are left unaltered, but the evidence offered at trial proves facts materially different from those alleged in the indictment," United States v. Zingaro, 858 F.2d 94, 98 (2d Cir. 1988) (quoting Gaither v. United States, 413 F.2d 1061, 1071 (D.C.Cir. 1969)). Whereas a constructive amendment per se violates the grand jury guarantee of the fifth amendment, a variance violates this guarantee only when the defendant can demonstrate prejudice. Id. Thus, where the indictment gives insufficient notice of the offense charged, the resulting prejudice requires reversal of the conviction. See United States v. Miller, 471 U.S. 130, 134, 105 S.Ct. 1811, 1814, 85 L.Ed.2d 99 (1985); see also United States v. Chestnut, 533 F.2d 40, 45 (2d Cir.) (defendant on notice when charged with successor to statute violated; conviction affirmed), cert. denied, 429 U.S. 829, 97 S.Ct. 88, 50 L.Ed.2d 93 (1976).

There was no constructive amendment here because neither the evidence nor the jury instructions modified the "essential elements of the offense charged," Mollica, 849 F.2d at 729, which is that transactions were fabricated for the purpose of being reported, and were reported on the specified tax returns. This case is unlike Mollica, where there was a constructive amendment because the court instructed the jury to consider the accusation of conspiracy to defraud the IRS "in the ascertainment, computation, assessment, and collection of revenues," but forgot to mention the object, "to wit: income taxes." Id. at 728. The object of the conspiracy, as instructed by the court here, was more detailed, specifying not only that the IRS was being defrauded of income taxes, but that the taxes were owed by Louis and Marie Attanasio for the years 1983 and 1984. Because defendants were not "convicted of an offense other than that charged in the indictment," id. at 729 (quoting Hathaway, 798 F.2d at 910), there was no constructive amendment of the indictment.

Nevertheless, some of the evidence at trial did differ from the facts alleged in the indictment. This suggests a variance. See Zingaro, 858 F.2d at 98. However, Mallon and LaMagra were not prejudiced by any variance between the facts alleged in the indictment and those proved at trial because the indictment in its entirety apprised them of the offenses charged. Therefore, any variance is at most harmless.

C. "Two-Inference" Jury Charge

The government concedes that the "two-inference" jury instruction was improper. The instruction explained that the inference favoring innocence must prevail when the inferences of guilt and innocence are equally balanced. We previously have condemned such a charge "because, standing alone, such language may mislead a jury into thinking that the government's burden is somehow less than proof beyond a reasonable doubt." United States v. Kahn, 821 F.2d 90, 93 (2d Cir. 1987); see also United States v. Hughes, 389 F.2d 535, 537 (2d Cir. 1968). While it may be error, it need not necessarily be harmful in light of "the district court's entire charge in th[e] case," Kahn, 821 F.2d at 92. Here, the judge instructed the jury several times on the reasonable doubt standard, including once immediately prior to the challenged instruction. We do not dismiss this claim lightly, in view of our recent decision in Kahn, Here, however, no appellant objected at trial to the "two-inference" charge, and the charge was "not such as to undermine the fundamental fairness of the trial and contribute to a miscarriage of justice," United States v. Young, 470 U.S. 1, 16, 105 S.Ct. 1038, 1047, 84 L.Ed.2d 1 (1985).

D. Remaining Contentions

We have considered appellants' remaining contentions and find them to be without merit.

CONCLUSION

The judgments of the district court are affirmed.