
    UNITED STATES of America, Appellee, v. Dov SHELLEF and William Rubenstein, Defendants-Appellants.
    Docket Nos. 06-1495-cr(L), 06-1710-cr(CON).
    United States Court of Appeals, Second Circuit.
    Argued: Dec. 18, 2006.
    Decided: Nov. 8, 2007.
    
      Andrew L. Frey, Mayer Brown LLP (Andrew H. Schapiro, Daniel B. Kirschner, Mayer Brown LLP, Stuart E. Abrams, Frankel & Abrams, of counsel), New York, NY, for Defendanb-Appellant Dov Shellef.
    Alan L. Zegas, Law Offices of Alan L. Zegas, Chatham, NJ (William Nossen, Law Offices of Alan L. Zegas, Chatham, NJ, and, Robert W. Gluck, Mandelbaum, Salsburg, Gold, Lazris & Discenza, P.C., New Brunswick, NJ, of counsel), for Defendant-Appellant William Rubenstein.
    S. Robert Lyons, Tax Division, Department of Justice, Washington, D.C., (Eileen J. O’Connor, Assistant Attorney General, Alan Hechtkopf, Karen M. Quesnel, Tax Division, Department of Justice, Washington, D.C., and Roslynn Mauskopf, United States Attorney for the Eastern District of New York, New York, NY, of counsel), for Appellee.
    Before: POOLER, SACK, and WESLEY, Circuit Judges.
   SACK, Circuit Judge:

The defendant Dov Shellef owned or operated several companies engaged in the distribution of industrial chemicals. The defendant William Rubenstein owned or operated Dunbar Sales, Inc., and Stevens Industries, Inc., which also distributed industrial chemicals and provided warehousing, packaging, labeling, and billing services to other distributors. The chemical at issue in this case-CFC-113-is exempt from excise taxes if its sale comports with applicable federal statutory and regulatory requirements. Notwithstanding the defendants’ representations to the manufacturers from whom they bought the chemical that the defendants would sell it in a manner that would render the sales excise-tax-free, some of Shellefs and Rubenstein’s sales of CFC-113 did not comply with at least one of these requirements. The government charged Shellef and Rubenstein jointly with conspiracy to defraud the IRS and wire fraud. The indictment also charged Shellef (but not Rubenstein) with 1) personal income tax evasion in 1996; 2) filing on behalf of one of his businesses a corporate tax return that was false insofar as it failed to report legitimate income in 1996; and 3) filing a corporate tax return on behalf of another of his businesses that was false insofar as it failed to report income in 1999. Shellef alone was also charged with money laundering associated with the alleged wire fraud. A jury convicted Shellef and Rubenstein on all charges against them.

On appeal, Rubenstein argues, as a threshold matter, that the 1996 tax charges against Shellef were improperly joined with the conspiracy to defraud and wire fraud charges against him. Shellef similarly argues that the 1996 tax charges should not have been joined with the other charges against him.

Under Rule 8 of the Federal Rules of Criminal Procedure, joinder of criminal charges is permissible when, inter alia, the charges are “based on the same act or transaction.” Fed.R.Crim.P. 8(a). Join-der of tax charges with non-tax charges under Rule 8 is therefore permissible if “the tax offenses arose directly from the other offenses charged,” such as when the funds derived from the acts underlying the non-tax charges “either are or produce the unreported income” that is the basis for the tax charges. United States v. Turoff, 853 F.2d 1037, 1043 (2d Cir.1988) (internal quotation marks and citations omitted). Even “if the character of the funds ... do[es] not convince us of the benefit of joining the[] two schemes in one indictment, other ovex-lapping facts or issues may.” Id. at 1043-44.

We conclude that the indictment improperly joined the 1996 tax evasion and false return counts against Shellef with the other charges against both defendants because the 1996 counts are not “based on the same act or transaction” as the other charges within the meaning of Rule 8. We further conclude, for reasons set forth below, that the joinder of Shellef and Ruben-stein as defendants in the indictment was also improper. Because the government has not established that the misjoinders of charges and defendants were harmless, we vacate the judgments of conviction and remand for further proceedings.

Shellef and Rubenstein raise several other issues on appeal that we need not decide in light of our disposition of the question of joinder: 1) the legal sufficiency of the wire fraud and conspiracy indictments; 2) the evidentiary sufficiency of the conviction for wire fraud; 3) the propriety of several evidentiary, rulings made by the district court; and 4) the propriety of the jury instructions. We nonetheless discuss all but the district court’s evidentiary rulings to guide the district court on retrial.

BACKGROUND

Because the jury returned a guilty verdict, the evidence presented to it is construed “in the light most favorable to the government.” United States v. Naiman, 211 F.3d 40, 46 (2d Cir.2000) (citation omitted). Except where noted below, the parties do not dispute the relevant material facts.

The Defendants

The defendant Dov Shellef owned or operated four companies: Poly Systems, Inc. (“Poly Systems”); PolyTuff, Ltd. (“PolyTuff’); PolyTuff USA, Inc. (“Poly-Tuff USA”); and Poly Systems USA, Inc. (“Poly Systems ÜSA”). Poly Systems was an entity located in and doing business from the United States, which sold and distributed defense-related materials, including aircraft manufacturing and maintenance products, primarily to the government of Israel. PolyTuff, an Israeli company, functioned as Poly Systems’s representative in Israel. Although nominal ownership of PolyTuff was transferred to one Avi Dolev in 1990, Shellef ran the company beginning no later than 1995, when, according to Shellef, Dolev “disappeared.” Test, of Dov Shellef, Trial Tr. 2270-71, July 14, 2005. PolyTuff USA was located in and doing business from the United States; it had been founded by Dolev in 1992 after the Israeli government refused to continue doing business with Shellef and Poly Systems. Poly Systems USA manufactured and sold industrial solvents.

Rubenstein is the executive vice president and a forty-five percent owner of two New Jersey-based companies, Dunbar Sales, Inc. (“Dunbar”), and Stevens Industries, Inc. (“Stevens”). The companies buy a variety of industrial chemicals and re-sell them to the United States and foreign governments. These entities also provide warehousing, packaging, labeling, shipping, and bill collection services. Ruben-stein provides day-to-day management for the companies.

In 1995, Rubenstein and Shellef began working together in an attempt to profit from an impending ban on domestic production of CFC-113. Their plan was to purchase a large volume of CFC-113 that had been produced and stockpiled in anticipation of the ban on production and to sell it to entities that would have difficulty obtaining it elsewhere thereafter.

In 1998, Stevens became a co-owner, with Shellef, of Poly Systems USA. That year, Shellef or his company Poly Systems transferred cash to Poly Systems USA as capital. Around that time, Shellef also invested in three unrelated real estate ventures that Rubenstein had undertaken.

Regulatory Regime Governing CFC-113

CFC-113 is a highly regulated, ozone-depleting industrial solvent commonly used to remove grease from metal. Global regulation of CFC-113 began in earnest following the ratification of the Montreal Protocol on Substances that Deplete the Ozone Layer (the “Montreal Protocol”) in 1987. Montreal Protocol, Sept. 16,1987, S. Treaty Doc. No. 100-10, 1522 U.N.T.S. 29. Pursuant to the Montreal Protocol, Congress sharply limited American production of CFC-113 as part of the Clean Air Act, 42 U.S.C. §§ 7401 et seq. The Act implemented a phased ban, 4 to be completed by 2000, of the “production and consumption” of the substance in the United States. See 42 U.S.C. § 7671c. Previously stockpiled CFC-113 could, however, still lawfully be used in the United States. As an incentive for discontinuance of such use, Congress imposed an excise tax on any CFC-113 “sold or used by the manufacturer ... thereof.” See 26 U.S.C. § 4681(a)(1) (imposing a tax on sales of ozone-depleting chemicals); 26 U.S.C. § 4682(a)(2) (including CFC-113 within the definition of ozone-depleting chemicals).

Congress carved out three exceptions to the applicability of the excise tax, two of which are relevant here. See 26 U.S.C. § 4682(d).

First, CFC-113 that has been “diverted or recovered in the United States as part of a recycling process (and not as part of the original manufacturing or production process)” is not subject to the tax. 26 U.S.C. § 4682(d)(1). Such diverted or recovered CFC-113 is known as “reclaimed CFC-113.” Newly manufactured CFC-113, by contrast, is referred to as “virgin CFC-113.”

Second, the statute exempts “sale[s] by the manufacturer or producer of [CFC-113] for export, or for resale by the purchaser to a second purchaser for export.” 26 U.S.C. § 4662(e)(1)(A); see also 26 U.S.C. § 4682(d)(3) (incorporating section 4662(e) by reference). The statutes and regulations thereunder impose three procedural requirements for a sale to qualify for this export exemption: 1) both parties must be registered with the Internal Revenue Service (“IRS”), see 26 C.F.R. § 52.4682-5(d)(l)(i)(B); 2) the purchaser must provide the manufacturer with a certificate containing a sworn statement from the purchaser that the CFC-113 will be exported, see 26 C.F.R. § 52.4682-5(d)(l)(i)(C), (d)(3); and 3) the manufacturer must receive proof of export within six months of the initial sale, see 26 U.S.C. § 4221(b) (requiring proof of export); 26 U.S.C. § 4662(e)(1)(B) (incorporating section 4221(b) by reference).

ElfAtochem CFC-113

In 1995, Rubenstein’s Stevens placed five purchase orders with Elf Atochem (“Elf’) for a total of 217,812 pounds of CFC-113 imported from an Elf affiliate in France (the “Elf CFC-113”). Elf initially charged Stevens $1,152,516.78 for the Elf CFC-113, which price included, in addition to a relatively modest base price, the applicable excise tax of $819,599.58. The parties stipulated before trial, however, that Rubenstein initially intended to export the Elf CFC-113, as he had represented to Elf that he would in order to negotiate an excise-tax-free agreement. Rubenstein further attempted to register with the IRS to satisfy his obligations under section 4682(d). Elf, which had previously paid the excise tax to the IRS on its quarterly return, took a credit for it on a subsequent return, and credited Rubenstein’s account for the previously invoiced tax.

Rubenstein exported nearly 190,000 pounds — or all but about 28,000 pounds— of the Elf CFC-113. In 1997, however, Rubenstein, with Shellefs help, began to sell the remaining Elf CFC-113 domestically for domestic use notwithstanding the fact that the original sales of any such Elf CFC-113 to Rubenstein’s companies would no longer qualify for the excise tax exemption that Rubenstein told Elf would apply to the entire purchase.

Shellef paid an employee of Marisol, Inc., a chemical solvent distributor, to refer Marisol’s domestic CFC-113 sales leads to Shellef. Among the prospects referred to Shellef under that arrangement were All Discount Laboratories (“All Discount”) and Custom Laboratories (“Custom”), both based in California.

Shellef used Rubenstein’s Elf CFC-113 to fill some of All Discount’s and Custom’s orders. On July 14, 1997, Shellef purchased four drums totaling 2,760 pounds of Elf CFC-113 from Rubenstein and resold them to AH Discount. In September and October 1997, Shellef made four shipments of the Elf CFC-113 to All Discount and Custom. Finally, on September 8, 1998, Shellef purchased Elf CFC-113 from Ru-benstein, this time reselling it to Marisol.

In sum, between July 1997 and September 1998, Shellef bought approximately 28,000 pounds of Elf CFC-113 from Ru-benstein and resold it domestically. For many of these sales, Rubenstein prepared documents — labels and invoices — falsely indicating that the Elf CFC-113 was reclaimed or was being shipped for export. The excise tax owing and unpaid on these sales of Elf CFC-113 totaled $136,482.

Allied Signal CFC-113

In 1995, Shellef sought virgin CFC-113 from Allied Signal Inc. (“Allied”), in the United States, purportedly for excise-tax-free resale abroad. Allied and Poly Sys-terns eventually executed a contract effective January 1, 1996 (the “Allied Contract”), under which Allied was required to manufacture 700,000 pounds of CFC-113 (the “Allied CFC-113”) for Poly Systems and store it until Poly Systems requested delivery. Poly Systems agreed to purchase and take delivery of all of the Allied CFC-113 sometime prior to December 31, 1997.

Under the Allied Contract, Poly Systems could sell the Allied CFC-113 only within a designated territory: Israel, Saudi Arabia, Syria, Egypt, and Jordan. Because the contract required that the Allied CFC-113 be exported, Allied agreed not to charge Poly Systems the excise tax. As set forth in Paragraph 8.A of the agreement, Poly Systems bore the risk of future government regulations prohibiting it from selling the CFC-113 so long as Allied spent at least twelve months after the effective date of the regulation “exercising] reasonable commercial efforts to sell [the Allied CFC-113] to other parties who are permitted to use [it],” with the proceeds of any such sale that exceeded the contract price to be divided equally by Poly Systems and Allied. Allied Contract, effective Jan. 1,1996, at 3 ¶ 8.A.

The Allied Contract required Poly Systems to pay an up-front $140,000 reservation fee, of which Rubenstein paid half in exchange for a share of the profits Poly Systems would earn selling Allied CFC-113 to the Israeli government. Although Rubenstein did not receive a share of Poly Systems’s profits from domestic sales of Allied CFC-113, he did store some in his warehouse in Bayonne, New Jersey, and shipped the product as Poly Systems directed.

Poly Systems’s initial sales were to the Israeli government. But Israel-like the United States, a signatory to the Montreal Protocol-was attempting to reduce its manufacture, importation, and use of ozone-depleting chemicals, including CFC-113. By December 1997, Israeli purchases of CFC-113, which had slowed in 1996, came to a halt. Shellef s orders with Allied followed the same pattern, but he did not then inform Allied of the regulatory change in Israel which might have invoked Paragraph 8.A.

Poly Systems and Allied consequently became involved in “a dispute around Poly Systems not taking the material on the schedule that it was required to under the original agreement.” Test, of Anne Madden, Trial Tr. 858:18-21, June 29, 2005. To resolve the dispute, Allied and Poly Systems amended the Allied Contract effective December 1, 1997 (“First Amended Allied Contract”). Under the First Amended Allied Contract, Poly Systems was required to order the remaining Allied CFC-113 by December 15,1997, but Allied was required to continue storing it through December 31, 1998. Allied also agreed to extend Poly Systems’s territorial exclusivity in the Middle East until December 31, 1999, if Poly Systems took possession of the Allied CFC-113 by December 31, 1998. The amendment incorporated all other consistent terms of the original October 1995 contract.

The amendment to the Allied Contract did not solve Shellefs biggest problem: The government of Israel, his best customer, was no longer importing CFC-113. Shellef did have other willing buyers of CFC-113 — Custom and All Discount, which began buying Elf CFC-113 in mid-1997 — but the First Amended Allied Contract prohibited Shellef from selling Allied CFC-113 to them. Still, knowing that Ru-benstein did not have enough Elf CFC-113 to fill the Custom and All Discount orders, Shellef negotiated another amendment to the Allied Contract on February 10, 1998, effective January 7, 1998 (“Second Amended Allied Contract”). Poly Systems now was required to purchase and take possession of the remaining Allied CFC-113-493,000 pounds — by June 30, 1998, but the price was reduced from $3.75 to $3.55 per pound. Shellef rejected Allied’s offer to terminate the contract if the Israeli government informed him that it would not order CFC-113 in 1998. The Second Amended Allied Contract stated that “from and after June 30, 1998, all price, volume, and other terms and conditions of sale of [CFC-113] by [Allied] to [Poly Systems] under the Contract shall not be as set forth in the Contract, but shall be as negotiated by the parties from time to time from and after June 30, 1998.” Second Amended Allied Contract, at 1 ¶ 1.

On June 3, 1998, Shellef sent his contact at Allied, Albert “Lou” Dorsey, a letter stating that Israel had adopted a law generally prohibiting CFC importation. The letter asserted, though, that there might be an exception for “previous importers” and that Shellef was negotiating with such an entity. Letter from Shellef to Dorsey dated June 3, 1998. He suggested that pending the outcome of those negotiations, a) Poly Systems would place orders with Allied before June 30 at the contract price; b) Poly Systems would buy at the regular market price after June 30; and c) Allied should “exercise reasonable commercial efforts” sell the remaining CFC-113 in accordance with Paragraph 8.A of the original contract. Id.; Allied Contract at 3 ¶ 8.A. Allied pressed Shellef to purchase all the remaining CFC-113 under the agreement and questioned the nature of the governmental regulation that would allow Shellef to invoke Paragraph 8.A. Shellef responded on June 19 by sending Allied a copy of a letter dated March 15, 1998, from an Israeli governmental official to Shellefs lawyer. It stated: “In principle, according to the Vienna Convention, Montreal Protocol, the import [sic] of ... CFC-113 is prohibited.” Test, of Lou Dorsey, Trial Tr. 711:17-19, June 28, 2005.

On October 5, 1998, Shellef offered to purchase all of the remaining Allied CFC-113 at a rate of one truckload per month, if Allied reduced the price to $1.60 per pound and continued his exclusive rights in the Middle East. Shellef told an Allied lawyer that “a window had opened up [in Israel] and he would be able to move some material at a lower price.” Test, of Anne Madden, Trial Tr. 883:17-18, June 29, 2005. Allied and Shellef agreed on a price of $1.75 per pound and, with other changes not relevant here, agreed that the “other terms and conditions of the Agreement, except to the extent they are inconsistent with the above provisions shall continue in full force and effect.” Letter from Dorsey to Shellef dated Oct. 28, 1998 (the “Autumn 1998 Agreement”).

Sometime after the February 1998 amendment became effective, but probably before June 1998, Custom stopped buying CFC-113 from Shellef. But during and after the course of the contractual dispute and subsequent negotiations, Shellef began selling Allied CFC-113 to All Discount, making two shipments in September 1998. Shellef asked Rubenstein to ship the Allied CFC-113 out of the Bayonne warehouse in which it had previously been stored, to remove any references to Allied on the drums, and to label the virgin Allied CFC-113 falsely as “reclaimed 113.” From October through December 1998, Shellef made four more shipments of Allied CFC-113 to All Discount.

In early 1999, Shellef began storing Allied CFC-113 with Five Star Enterprises (“Five Star”), a consignee freight forwarder in California. Shellef directed Five Star to follow instructions given by Ruben-stein. On March 12, 1999, Rubenstein’s employee, at Shellefs direction, shipped thirty-six drums of the Allied CFC-113 from Rubenstein’s New Jersey warehouse to Five Star’s California warehouse. Five Star then made periodic shipments of the Allied CFC-113 to All Discount when instructed to do so by Shellef. Other shipments of Allied CFC-113, including sixty drums on February 7, 2000, were also made to Five Star for distribution to All Discount.

Beginning on March 9, 2000, Shellef also sold Allied CFC-113 to Mid-Atlantic Chemical, Inc. (“Mid-Atlantic”), a Pennsylvania-based domestic distributor of CFC-113. Shellef told the president of Mid-Atlantic that excise taxes “had been taken care of’ on the Allied CFC-113. Test, of Theodore Stepanoff, Trial Tr. 1250:9-14, June 29, 2005. Mid-Atlantic’s first purchase of Allied CFC-113 from Shellef was resold by MidAtlantie to EM Science in Ohio.

In April 2000, Shellef contacted EM Science directly to offer ten drums of Allied CFC-113 “left over from a project in California.” Test, of Ronald Wizda, Trial Tr. 523-24, June 27, 2005. Shellef offered it at a tax-paid price. EM Science wanted to test the quality of Shellefs product before placing an order. On May 18, 2000, Shel-lef directed Rubenstein to ship one drum of Allied CFC-113 to EM Science, but to make sure to remove a label falsely indicating that it was reclaimed and attach instead a label correctly indicating that the product was virgin CFC-113 produced by Allied. EM Science decided to satisfy its additional CFC-113 requirements through Mid-Atlantic, not through Shellef.

Shellef sold Allied CFC-113 on the domestic market each year from 1998 through 2000, with the applicable but unpaid excise tax rate varying from year to year. All told, Shellef sold 30,360 pounds of Allied CFC-113 domestically in 1998; the excise tax due on these sales totaled $162,729.60. In 1999, Shellef sold 198,580 pounds domestically, resulting in an unpaid excise tax in the amount of $1,135,877.60. Finally, in 2000, Shellefs domestic sales of 73,252 pounds of CFC-113 required a total excise-tax payment of $445,372.16 that was never paid. Shellef never sent Allied any documentation regarding any of the domestic sales of its product.

1996 Tax Charges

Two of the tax charges concern filings with the IRS for the year 1996 — Shellefs personal return and the PolyTuff USA corporate return filed by Shellef. Shellef had hired an accountant, Stephen Stein, to prepare corporate tax returns for Poly Systems, Poly Systems USA, and PolyTuff USA for that year. Stein had also prepared Shellefs personal income tax returns. Shellef gave Stein copies of “Quicken” records that Shellef kept, but he never gave Stein original invoices or similar backup documents to substantiate the information contained in the Quicken documents.

For PolyTuff USA’s 1996 fiscal year, which ended on February 28, 1997, Shel-lefs Quicken records, and the PolyTuff USA tax return prepared by Stein, revealed gross receipts of $683,639. After expenses, this amounted to a taxable income of $10,547. Stein reconciled the 1996 PolyTuff USA Quicken information with records from checking and money market accounts PolyTuff USA held at First Bank of the Americas. But Shellef did not inform Stein of a PolyTuff USA account held at Marine Midland Bank in which PolyTuff USA had deposited four checks in the total amount of $1,942,113.62 during fiscal year 1996. The reported gross receipts therefore understated actual gross receipts by nearly $2 million. After accounting for unreported expenses, PolyTuff USA owed $288,621.58 in taxes for 1996, instead of the $1,582 it claimed to owe on its return.

Shellefs personal income tax return for 1996, also prepared by Stein, reported total income of $77,446 and taxable income of $53,996. But Shellef hid personal bank accounts from Stein. Because of undisclosed transactions involving these accounts and PolyTuff USA, Shellefs taxable income for 1996 in fact was $957,326— $903,330 more than the $53,996 Shellef reported. Shellef owed $344,152 more in personal income tax for 1996 than the $9,900 he had reported and paid.

1999 Tax Charge

By 1998, Shellef was working with a different accountant at Stem’s firm — Stephen Kashinsky. Kashinsky prepared Poly Systems’s original 1999 corporate tax return. Based on the Quicken records and bank statements that Shellef gave him, Kashinsky reported gross receipts of $986,224.

But Shellef did not tell Kashinsky about accounts held by Poly Systems at North Fork Bank (“North Fork”) and Commercial Bank of New York (“CBNY”). In 1999, All Discount paid Poly Systems $662,400 for Allied CFC-113, which it transferred by wire into the undisclosed Poly Systems account at CBNY. Poly Systems also deposited two checks in the total amount of $120,216 into its undisclosed North Fork account. Poly Systems’s 1999 corporate tax return thus under-reported gross receipts by $782,616. When Shellef became aware of an FBI investigation of his business affairs, he replaced Kashinsky with Michael Maddaloni, who had been preparing Poly Systems USA’s filings since Rubenstein made his investment in that company. Shellef filed an amended return for Poly Systems that added $760,701 to the original return’s report of $986,224 in gross receipts, $21,915 less than the $782,616 he had failed to report.

Shellef also withheld information from Kashinsky about personal foreign bank accounts-one at Credit Suisse in Switzerland and the other at Bank Leumi in Israel. He conducted three wire transfers in the total amount of $450,240 out of Poly Systems’s CBNY account and into the Credit Suisse and Bank Leumi accounts. The original return did not reflect these transactions. The amended return showed most of these transfers as loans from Poly Systems to Shellef. Shellef repaid the loans with interest.

The Indictment

On June 24, 2003, a grand jury in the United States District Court for the Eastern District of New York returned a ninety-one count indictment against Shellef and a forty-six count indictment against Rubenstein. Count One charges them jointly with conspiring to impede the IRS’s collection of excise taxes in violation of 18 U.S.C. § 371, based on their domestic sales of Elf and Allied CFC-113. Shellef and Rubenstein were also charged jointly in Counts Five through Fifty with wire fraud, in violation of 18 U.S.C. § 1343. Those counts rested on two alternative theories of fraud based on Shellefs alleged promise to export all the Allied CFC-113: 1) absent Shellefs alleged misrepresentation about the CFC-113’s destination, Allied would have charged Poly Systems for the excise tax due on domestic sales of virgin CFC-113; and 2) absent the alleged misrepresentation, Allied would not have sold Shellef the CFC-113. Rubenstein’s alleged role in the wire fraud was to store, re-label, and ship the Allied CFC-113 to domestic customers at Shellefs direction. Shellef and Rubenstein allegedly used wire communications to transmit shipping instructions, invoices, and payments they received for domestic sales as part of their plan.

The remainder of the counts in the indictment charge only Shellef. Count Two alleges that Shellef violated 26 U.S.C. § 7206(1) by subscribing to false statements regarding the gross receipts reported in PolyTuff USA’s 1996 tax return. Count Three alleges that Shellef evaded personal income taxes for 1996 by understating his taxable income and the tax due, a violation of 26 U.S.C. § 7201. Count Four charges Shellef with another violation of section 7206(1), this one arising out of the alleged understatement of Poly Systems’s gross receipts on its 1999 corporate tax return.

In addition to these tax charges, Shellef was indicted on forty-one counts of money laundering, based on his actions underlying the conspiracy and wire fraud counts. The first five, Counts Fifty-One through Fifty-Five, allege violations of 18 U.S.C. § 1956(a)(1)(A)® arising out of Shellefs use of proceeds from domestic sales of CFC-113 to buy more Allied CFC-113. Counts Fifty-Six through Ninety-One allege violations of 18 U.S.C. §§ 1956(a)(l)(A)(ii) and (B)(i), arising out of Shellefs transfer of proceeds from domestic CFC-113 sales to U.S. and foreign bank accounts.

District Court Proceedings

Prior to trial, Shellef moved to dismiss the conspiracy, wire fraud, and 1999 tax counts for failure to allege offenses and to sever all tax counts from the other counts under Rule 8 of the Federal Rules of Criminal Procedure. Rubenstein joined in seeking the relief sought by Shellef. The district court denied the motions.

The trial began on June 20, 2005. The government’s evidence supporting the conspiracy and wire fraud charges — and, by extension, the money laundering charges based on the conspiracy and wire fraud counts — came principally from two witnesses, Allied’s Albert Dorsey and Anne Madden. They testified, inter alia, that Shellef obligated himself in the Autumn 1998 Agreement to continue to confine himself to export sales. Shellef s defense to these charges rested in large part on his assertion that he did not, under the Autumn 1998 Agreement or otherwise, undertake to export the Allied CFC-113 after the original contract expired on June 30, 1998.

Although most of the trial explored Shellefs and Rubenstein’s dealings with Elf and Allied, substantial portions related to the 1996 personal tax evasion and false return charges against Shellef. Indeed, roughly half of the government’s cross-examination of Shellef focused on the 1996 tax evasion and false return charges.

On July 28, 2005, the jury returned general verdicts of guilty against both defendants on all counts of which each was charged. The district court thereafter sentenced Shellef principally to seventy months’ imprisonment and three years of supervised release. The district court sentenced Rubenstein principally to eighteen months’ imprisonment and three years of supervised release. Shellef and Ruben-stein were ordered to pay $1,880,461 in restitution. The district court also entered a final order of forfeiture requiring Shellef to forfeit $1,350,650.

This appeal followed. By Order of this Court dated December 19, 2006, the district court released the defendants on bond pending appeal.

DISCUSSION

I. Jurisdiction

The district court had jurisdiction over the prosecution of Shellef and Rubenstein pursuant to 18 U.S.C. § 3231 because they were charged with violating federal criminal laws. The district court entered judgments of conviction against Rubenstein in March 2006 and against Shellef in April 2006. We have jurisdiction over the appeal of such final judgments under 28 U.S.C. § 1291.

II. Basis for Vacatur and Remand

The defendants argue that the 1996 tax evasion and false return counts against Shellef were improperly joined with the remainder of the counts in the indictment. The government defends the joinder on the ground that “the charges were ‘based on the same act or transaction’ as the other charges the jury was to consider.” Gov’t Br. at 51.

We review the propriety of join-der de novo. United States v. Feyrer, 333 F.3d 110, 113 (2d Cir.2003). “[T]he propriety of Rule 8 joinder is subject to full appellate review, and where joinder should not have been permitted, a conviction must be reversed, unless failure to sever was harmless error.” United States v. Attanasio, 870 F.2d 809, 815 (2d Cir.1989) (internal quotation marks and citations omitted).

Federal Rule of Criminal Procedure 8 sets forth when joinder is appropriate in criminal cases:

Joinder of Offenses or Defendants
(a) Joinder of Offenses. The indictment or information may charge a defendant in separate counts with 2 or more offenses if the offenses charged' — -whether felonies or misdemeanors or both — are of the same or similar character, or are based on the same act or transaction, or are connected with or constitute parts of a common scheme or plan.
(b) Joinder of Defendants. The indictment or information may charge 2 or more defendants if they are alleged to have participated in the same act or transaction, or in the same series of acts or transactions, constituting an offense or offenses. The defendants may be charged in one or more counts together or separately. All defendants need not be charged in each count.

Fed R.Crim. P. 8. Thus, while Rule 8(a) allows joinder of offenses that are of “the same or similar character,” Rule 8(b) does not allow joinder of defendants on that basis alone-they must be “alleged to have participated in the same act or transaction, or in the same series of acts or transactions.” Id.

The parties devote considerable attention to the question whether Rule 8(a) or Rule 8(b) applies when a defendant in a multi-defendant, multi-count prosecution such as the one against Shellef challenges the joinder of a count in which he is the only defendant charged. But the government explicitly defends both the joinder under Rule 8(a) of the charges against Shellef and the joinder under Rule 8(b) of defendants only on the grounds that the 1996 tax charges “are ‘based on the same act or transaction’ as the other charges the jury was to consider.” Gov’t Br. at 51. It further asserts that all of the charges “share a common nucleus, the sale of the CFC-113.” Gov’t Br. at 51. The government thus appears also to rely for joinder of offenses under Rule 8(a) on the grounds that the charged offenses “are connected with or constitute parts of a common scheme or plan,” Fed.R.Crim.P. 8(a), and for joinder of defendants under Rule 8(b) on the parallel grounds that the defendants “participated ... in the same series of acts or transactions, constituting an offense or offenses,” Fed.R.Crim.P. 8(b). Cf. United States v. Halper, 590 F.2d 422, 430 (2d Cir.1978) (justifying joinder under the “common scheme or plan” clause because it saves the government from having to “prov[e] what is essentially the same set of facts more than once” and the defendant from “defending more than once against what are essentially the same, or at least connected, charges”).

Critically, the government does not defend the joinder of offenses under Rule 8(a)’s “same or similar character” clause. See United States v. Turoff, 853 F.2d 1037, 1042-43 (2d Cir.1988) (concluding that Rule “8(b) provides a more restrictive test” because “[u]nlike Rule 8(a), Rule 8(b) does not permit joinder ... solely on the ground that the offenses charged are of ‘the same or similar character’ ”). If, then, the charges against Shellef alone are not “based on the same act or transaction” or “are [not] connected with or constitute parts of a common scheme or plan,” Fed.R.Crim.P. 8(a), and the charges against both Shellef and Rubenstein are not based on “the same act or transaction, or [o]n the same series of acts or transactions,” Fed.R.Crim.P. 8(b), both the joinder of charges and the joinder of defendants were improper.

A. Joinder of Charges against Shellef

1. Propriety of Joinder. There are three tax charges against Shellef. Two of them arise from Shellefs 1996 tax returns (the “1996 Tax Counts”). First, Shellef is charged with falsely reporting the gross receipts on PolyTuff USA’s 1996 corporate income tax return (the “PolyTuff Tax Count”). Second, he is charged with misstating his taxable income on his 1996 personal income tax return (the “Personal Tax Count”). Third, he is charged with falsely reporting gross receipts on Poly Systems’s corporate income tax return in 1999 (the “1999 Tax Count” or the “Poly Systems Tax Count”). As noted, these tax counts are joined with several non-tax counts charging both Shellef and Rubenstein with conspiracy and wire fraud and charging Shellef alone with money laundering. Shellef contends that the 1996 Tax Counts should not have been joined with the remaining counts, including the 1999 Tax Count.

We apply a “commonsense rule” to decide whether, in light of the factual overlap among charges, joint proceedings would produce sufficient efficiencies such that joinder is proper notwithstanding the possibility of prejudice to either or both of the defendants resulting from the joinder. See Turoff, 853 F.2d at 1044 (“applying a commonsense rule to these facts” to determine whether “a reasonable person would easily recognize the common factual elements that permit joinder”); see also id. at 1042 (recognizing that the tests for joinder “reflect[] a policy determination that [in some circumstances,] gains in trial efficiency outweigh the recognized prejudice that accrues to the accused”). For example, counts might be “connected” if one of the offenses “depend[s] upon []or necessarily l[eads] to the commission of the other,” or if proof of one act “constitute[s][ ]or depend[s] upon proof of the other.” Halper, 590 F.2d at 429.

“Tax counts may be joined with non-tax counts where it is shown that the tax offenses arose directly from the other offenses charged.” Turoff, 853 F.2d at 1043. “The most direct link possible between non-tax crimes and tax fraud is that funds derived from non-tax violations either are or produce the unreported income.” Id. Thus, if a defendant is charged with fraud, the government may prosecute the defendant for fraud and for not paying taxes on the profits produced by the alleged fraud jointly. And “if the character of the funds derived do not convince us of the benefit of joining these two schemes in one indictment, other overlapping facts or issues may.” Id. at 1043-14.

Here, the Personal Tax Count and the PolyTuff Tax Count against Shellef might have been properly joined with an indictment charging the 1999 Tax Count because there are common facts concerning Shel-lefs relationship with Stein and Kashin-sky’s accounting firm, which handled both his 1996 and 1999 tax returns. And inasmuch as the schemes underlying the non-tax counts against Shellef and Rubenstein generated the allegedly unreported 1999 income of Poly Systems that formed the basis for the 1999 Tax Count against Shel-lef, it seems likely that the 1999 Tax Count against Shellef could have been properly joined with an indictment charging only the conspiracy, wire fraud, and money laundering schemes against Shellef — the unreported 1999 income was produced by those schemes. See United States v. Biaggi, 909 F.2d 662, 676 (2d Cir.1990) (holding that tax counts were properly joined with conspiracy counts because most of the unreported income was produced by the conspiracy).

The funds generated by the wire fraud, money laundering, and conspiracy schemes, however, were unrelated to the unreported income that was the basis for the 1996 Tax Counts. Indeed, the alleged 1996 tax violations took place before the conspiracy and wire fraud allegedly began. The government’s contention that all the charges “share a common nucleus, the sale of the CFC-113,” Gov’t Br. at 51, paints the allegations with too broad a brush. Even assuming that PolyTuff USA’s unreported gross receipts and Shellefs unreported personal income derived entirely from CFC-113 sales (a fact about which the record is silent), the fact that the businesses that produced the 1996 unreported income were also subsequently used to perpetrate the alleged conspiracy and wire fraud does not justify a conclusion that the offenses charged are “based on the same act or transaction, or are connected with or constitute parts of a common scheme or plan” under Rule 8(a). Fed R.Crim. P. 8(a); see also Halper, 590 F.2d at 429 (rejecting the joinder of income tax counts with Medicaid fraud counts, even though the unreported income was generated by the same business that allegedly committed the Medicaid fraud, because the unreported income may have been produced by legitimate activities of the business unrelated to the fraud).

We can find no other link between the 1996 Tax Counts and the other charges sufficient to justify joinder of all of the counts. The gravamen of the government’s case with respect to the wire fraud, money laundering, conspiracy, and 1999 tax offenses is that Shellef and Rubenstein conspired to obstruct the IRS’s collection of the excise tax due on their sales of CFC-113 by misrepresenting to Allied and Elf their intent to resell the product abroad. The only common factual elements between those charges and the 1996 Tax Counts is that Shellef purchased CFC-113 from Allied and that Shellef used Stein and Kashinsky’s accounting firm from 1996 through 1999. Elements of the 1996 Tax Counts that are not common to the conspiracy, wire fraud, money laundering, and 1999 tax counts include that Shel-lef made sales to the government of Israel in 1996; that PolyTuff USA deposited these funds in an undisclosed Marine Midland account; that Shellef held an undisclosed personal account at Citibank to which he diverted corporate profits; and that he omitted the funds from his tax returns. Elements of the conspiracy, wire fraud, money laundering, and 1999 tax counts that are not common to the 1996 Tax Counts include that the Israeli government ceased importing CFC-113 in 1997; that Shellef renegotiated his contract with Allied on more than one occasion; that Rubenstein purchased CFC-113 from Elf; that Shellef and Rubenstein sold CFC-113 domestically; and that they misrepresented to their domestic buyers that the excise tax had been paid.

Requiring that the 1996 Tax Counts be tried separately from the remaining counts, moreover, would not require that the government “prov[e] what is essentially the same set of facts more than once” and Shellef to “defend[] more than once against what are essentially the same, or at least connected, charges.” Halper, 590 F.2d at 430. Because “[Commission of [the alleged wire fraud and conspiracy] neither depended upon nor necessarily led to the commission of’ the alleged 1996 tax misconduct and “proof of the one act neither constituted nor depended upon proof of the other,” joinder was improper. Id. at 429.

The charges are thus not “based on the same act or transaction, [and] are [not] connected with [and do not] constitute parts of a common scheme or plan” under Rule 8(a). Cf. Biaggi, 909 F.2d at 676 (“Proof of one scheme was helpful to a full understanding of the other.”). Although the 1996 Tax Counts may be relevant to determining whether Shellef possessed the requisite mens rea for the 1999 Tax Count, the 1996 Tax Counts and the non-tax counts are not sufficiently “unified by some substantial identity of facts or participants,” nor do they “arise out of a common plan or scheme.” Attanasio, 870 F.2d at 815 (quoting United States v. Porter, 821 F.2d 968, 972 (4th Cir.1987), cert. denied, 485 U.S. 934, 108 S.Ct. 1108, 99 L.Ed.2d 269 (1988)) (finding joinder appropriate where two contemporaneous conspiracies “shared a common purpose” and included “an overlap of participants and acts”).

We do not think, then, that the 1999 Tax Count — which might have been joined with either the 1996 Tax Counts or the conspiracy, wire fraud, and money laundering counts — provides an adequate link between the 1996 Tax Counts and the non-tax counts to justify joinder of all the charges against Shellef. The 1996 Tax Counts therefore should not have been joined with the remaining counts.

2. Harmlessness of Misjoin-der as to Shellef. Erroneous joinder “requires reversal only if the misjoinder results in actual prejudice because it ‘had substantial and injurious effect or influence in determining the jury’s verdict.’ ” United States v. Lane, 474 U.S. 438, 449, 106 S.Ct. 725, 88 L.Ed.2d 814 (1986) (quoting Kotteakos v. United States, 328 U.S. 750, 776, 66 S.Ct. 1239, 90 L.Ed. 1557 (1946)); see also id. at 450, 106 S.Ct. 725 (concluding that the error in that case was harmless because the evidence of guilt was overwhelming, limiting instructions were given, and the evidence on the misjoined count would have been admissible in a trial on the remaining counts). In determining whether the error was harmless, we inquire whether “evidence tending to prove the charge that should have been severed would nevertheless have been admissible at the trial of the objecting [jdefendant, and was admitted subject to appropriate limiting instructions.” Attanasio, 870 F.2d at 815 (quoting 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)) (internal quotation marks omitted). “The burden of establishing harmlessness is on the government.” United States v. Quattrone, 441 F.3d 153, 181(2d Cir.2006). We must examine whether the misjoinder was harmless with respect to the jury’s conviction of Shellef on each count.

a. The non-tax counts

We conclude that misjoinder of the tax and non-tax counts was not harmless with respect to Shellefs convictions on the non-tax counts. Had Shellef been tried on only the non-tax counts and the 1999 Tax Count, some of the evidence related to the 1996 Tax Counts might have been admissible for the limited purpose of establishing Shellefs mental state with respect to the 1999 Tax Count. See United States v. Bok, 156 F.3d 157, 165 (2d Cir.1998) (“[W]e have often explained [that] a defendant’s past taxpaying record is admissible to prove willfulness circumstantially.”); cf. Fed.R.Evid. 404(b) (“Evidence of other crimes, wrongs, or acts” may be admissible to prove, inter alia, “intent, ... knowledge, ... or absence of mistake or accident. ...”).

But other-acts evidence admissible under Rule 404(b) is subject to exclusion under Rule 403, which provides that evidence “may be excluded if its probative value is substantially outweighed by the danger of unfair prejudice.” Fed.R.Evid. 403; see also United States v. Myerson, 18 F.3d 153, 166 (2d Cir.1994) (recognizing that “[rjelevant evidence of a defendant’s prior bad acts [may be] admissible under Rule 404(b) ... so long as that evidence is not substantially more prejudicial than probative under Rule 403”). We think that the risk of unfair prejudice would have been excessive if evidence of the 1996 Tax Counts were to have been admitted in a trial on the non-tax counts and the 1999 Tax Count. A danger generally associated with other-acts evidence is that the jury will understand it to suggest that the defendant is predisposed to engage in a particular type of criminal activity. See Fed. R.Evid. 404(b) (providing that other-acts evidence “is not admissible to prove the character of a person in order to show action in conformity therewith”). In this case, there are at least two concerns about the other-acts evidence that would warrant its exclusion. First, there is the danger that the jury may improperly apply the other-acts evidence to the non-tax counts even though it is admissible only as to the 1999 Tax Count. The risk is that the jury would reason that if Shellef was willing to lie to the IRS in 1996, he would be willing subsequently to lie to others, including Allied and Elf personnel. Second, because here the other-acts evidence relates to Shellefs alleged deceit, there is an additional risk: The jury might have interpreted the 1996 Tax Counts evidence as an indication of Shellefs general mendacity relevant to the remaining counts and thereby discount his testimony unrelated to the tax counts.

Perhaps, as in Attanasio, an instruction strictly limiting the jury’s use of the evidence admitted as to the 1996 Tax Counts to that which is permissible — to negate the inference that the misstated gross receipts on the 1999 Poly Systems return were the product of mere mistake — -would have helped cure the prejudice. But no such instruction was given here. See Attanasio, 870 F.2d at 815 (noting that the district judge “gave appropriate limiting instructions to the jury” to narrow evidence admitted under Rule 404(b) to the defendant’s intent and motive). Since no limiting instruction was given, the evidence as to the 1996 Tax Counts would not have been admissible in a trial on all the other counts. We therefore conclude that the misjoinder of the 1996 Tax Counts was not harmless error as to the non-tax counts.

b. The 1996 Tax Counts

Prejudicial misjoinder of the charges is, in this case, two-way street. Just as the introduction of evidence as to elements of the 1996 Tax Counts was prejudicial to jury deliberation on the conspiracy, wire fraud, and money laundering counts, introduction of evidence as to elements of the conspiracy, wire fraud, and money laundering counts was prejudicial to jury deliberation on the 1996 Tax Counts. After hearing evidence of the conspiracy, wire fraud, and money laundering counts, the jury may have thought that Shellef was predisposed to commit crimes of deceit like those alleged in the 1996 Tax Counts. No limiting instruction was given that would have been adequate to protect against these risks. See Attarnasio, 870 F.2d at 815.

c. 1999 Tax Count

We conclude, finally on this score, that because of the misjoinder, the jury’s conviction of Shellef on the 1999 Tax Count also cannot stand. Although evidence relating to the 1996 Tax Counts and the non-tax counts is admissible as to the 1999 Tax Count, a limiting instruction was required to prevent the jury from improperly considering such evidence as demonstrating Shellefs propensity to commit crimes of deceit. See Bok, 156 F.3d at 165 (“[W]e have often explained [that] a defendant’s past taxpaying record is admissible to prove willfulness circumstantially.”); Attanasio, 870 F.2d at 815. The district court included an instruction of this sort, but it expressly related only to “evidence of acts of the defendants which may be similar to those charged in the indictment, but which were committed on other occasions.” Trial Tr. 3146:13-16, July 25, 2005. Without a similar limiting instruction applicable to the acts charged in the indictment, however, the government has not demonstrated that the evidence relating to the 1996 Tax Counts or the non-tax counts did not result in actual prejudice to the jury’s deliberation. As a result, Shellefs judgment of conviction on the 1999 Tax Count also must be vacated.

B. Sufficiency of the Evidence of Conspiracy as to Shellef

Shellef also argues that the evidence presented failed to support his conviction for conspiring to defraud the IRS, and that therefore his conviction must be reversed rather than vacated.

Shellef contends that all of the evidence is consistent with a motive to evade Allied’s exclusive domestic distributorship agreements by deceiving the company into thinking that he would not sell the CFC-113 domestically. Because that scheme did not have as a necessary result the perpetration of a fraud on the IRS and there is no additional evidence of actions that would not be explained by a motive to deceive Allied instead of the IRS, Shellef argues, we are required to vacate his conviction for conspiracy.

But the government introduced considerable evidence of conduct by Shellef and Rubenstein that supports the inference that they intended to avoid payment of the excise tax entirely, rather than only to trick Allied into selling them CFC-113. For example, Shellef represented to his buyers that the excise tax had been paid; Rubenstein prepared documents indicating that the material was either reclaimed or for export only; and Shellef charged his customers just below Allied’s tax-paid rate (and significantly above the tax-free rate Shellef paid). All this was done after they had acquired the CFC-113, and hence is not explainable solely by “the objective of obtaining the chemical from Allied.” Shellef Br. at 51. The evidence “allow[ed] the jury to reasonably infer that each essential element of the crime charged,” United States v. D’Amato, 39 F.3d 1249, 1256 (2d Cir.1994), including the “inten[t] to impede or obstruct the IRS from carrying out its functions,” Gurary, 860 F.2d at 525, “has been proven beyond a reasonable doubt,” D’Amato, 39 F.3d at 1256.

In any event, even if the evidence was consistent with a motive to defraud Allied, it is also consistent with a motive to defraud the IRS. Because we must draw all inferences in favor of the verdict, United States v. Naiman, 211 F.3d 40, 46 (2d Cir.2000), the challenge fails.

C. Joinder of Charges against Ruben-stein

For many of the same reasons that there was a prejudicial misjoinder of the 1996 Tax Counts with the conspiracy, wire fraud, and money laundering counts as they relate to Shellef, a fortiori, the conspiracy and wire fraud counts against Rubenstein were prejudicially misjoined with the 1996 Tax Counts against Shellef. The indictment alleged that Shellef and Rubenstein devised and executed the wire fraud and conspiracy schemes together, but, as we have explained, the connection between that scheme and the 1996 Tax Counts is too tenuous to justify joinder under Rule 8. Moreover, just as the join-der of the 1996 Tax Counts with the non-tax counts against Shellef may have materially and improperly influenced the jury’s deliberations on the non-tax counts as to Shellef, it also may have materially and improperly influenced the jury’s deliberations on the wire fraud and conspiracy counts as to Rubenstein. Indeed, the potential for prejudice arising from misjoin-der is arguably greater as for Rubenstein than Shellef, not only because he had no connection at all with the 1996 Tax Count, but also because he chose not to testify yet may have suffered from any adverse credibility determinations made by the jury regarding Shellef s testimony. We therefore vacate the jury’s conviction of Rubenstein for wire fraud and conspiracy, too.

III. Issues on Remand

Because of the prejudicial misjoinder of charges against the defendants, we must vacate and remand the case to the district court for further proceedings. Because several other issues asserted as bases for vacatur of the defendants’ judgments of conviction have been fully briefed and argued, and because they are likely to arise again on remand and retrial, we address them here even though their resolution is not strictly necessary in order to decide this appeal.

A. Conspiracy to Defraud the IRS

Count One of the indictment charged that Shellef and Rubenstein conspired to defraud the IRS. See 18 U.S.C. § 371 (rendering it a crime to conspire “to defraud the United States, or any agency thereof in any manner or for any purpose”). Shel-lef and Rubenstein challenge the sufficiency of the indictment and the jury instructions on this count. We conclude that their challenges are without merit.

1. Sufficiency of the Indictment Shellef contends that the acts alleged in the indictment do not constitute a conspiracy to defraud the IRS because there is no allegation that he misled Allied or Elf regarding the IRS registration number or certificates of export required to make CFC-113 sales excise-tax free. Without such a misrepresentation, the CFC-113 remained taxable and Allied and Elf should have charged Shellef and Rubenstein the applicable excise taxes. Only Allied and Elf are guilty of failure to pay excise taxes.

The government responds that the likely success of the alleged conspiracy is irrelevant. All that is required is that the indictment allege that Shellef and Ruben-stein agreed to defraud the IRS, that they participated knowingly and voluntarily in the conspiracy, and that at least one of them committed an overt act in furtherance of the conspiracy. Because the indictment meets these requirements, the government argues, it is legally sufficient.

“The sufficiency of the indictment is a matter of law that is reviewed de novo.” United States v. Pirro, 212 F.3d 86, 92 (2d Cir.2000). The elements of a conspiracy to defraud the United States (also known as a “defraud clause conspiracy”) are “ ‘(1) [that defendant] entered into an agreement (2) to obstruct a lawful function of the government (3) by deceitful or dishonest means and (4) at least one overt act in furtherance of the conspiracy.’ ” United States v. Ballistrea, 101 F.3d 827, 832 (2d Cir.1996) (quoting United States v. Caldwell, 989 F.2d 1056, 1059 (9th Cir.1993)) (brackets in original). The “indictment charging a defraud clause conspiracy [must] set forth with precision the essential nature of the alleged fraud.” United States v. Helmsley, 941 F.2d 71, 90 (2d Cir.1991) (internal quotation marks and citations omitted).

Here, the “essential nature of the alleged fraud” was that Shellef and Ruben-stein misled manufacturers about the taxable status of their transactions. Whether the manufacturers themselves proceeded to mislead the IRS is immaterial. All that is necessary is that the scheme had the object of making it more difficult for the IRS to carry out its lawful functions and that the scheme depend on “dishonest or deceitful means.” See Ballistrea, 101 F.3d at 831-32 (“[Title 18 U.S.C. § 371] covers acts that interfere with or obstruct one of [the United States’] lawful governmental functions by deceit, craft or trickery, or at least by means that are dishonest, even if the Government is not subjected to property or pecuniary loss by the fraud” (citations and quotation marks omitted; second brackets in original)). Shellef and Ruben-stein’s scheme would have made it more difficult for the IRS to collect taxes on the CFC-113 transactions because Allied and Elf were allegedly misled by Shellef and Rubenstein as to the chemical’s destination. Thus misinformed, Allied and Elf could be expected, unwittingly or otherwise, to mislead the IRS about the taxable status of their CFC-113 sales.

Shellef argues that because Allied and Elf, not Shellef or Rubenstein, were under a duty to report the transactions to the IRS and pay the taxes, and because the transactions were taxable unless further misrepresentations were made, either by him or the manufacturers, he cannot be convicted under 18 U.S.C. § 371. But a defendant need not have a duty to report transactions or pay taxes to be convicted of a conspiracy to defraud the IRS with respect to those reports or payments. See United States v. Nersesian, 824 F.2d 1294, 1313 (2d Cir.), cert. denied, 484 U.S. 958, 108 S.Ct. 357, 98 L.Ed.2d 382 (1987) (“[T]he fact that [the defendant] ... had no duty to report [the] transactions ... is not the operative issue as to whether he agreed to unlawfully defraud the United States by impairing and obstructing [the IRS’s] lawful governmental function[] of collecting data....”). Nor can Shellef avoid the reach of the conspiracy statute by arguing that his scheme would fail because other requirements for tax-free treatment-certification of export and IRS registration-would not be satisfied. “[T]he illegality of [a conspiracy] does not depend upon the achievement of its goal” and it therefore “does not matter that the ends of the conspiracy were from the beginning unattainable.” United States v. Giordano, 693 F.2d 245, 249 (2d Cir.1982) (citations omitted).

Shellef and Rubenstein’s scheme, as alleged in the indictment, is similar to that of the defendants in Nersesian, 824 F.2d at 1309-13. Nersesian involved, among other things, the requirement under the Bank Secrecy Act, 31 U.S.C. § 5311 et seq., that banks report currency transactions exceeding $10,000 in a single day. See Nersesian, 824 F.2d at 1310. The defendants structured their transactions so the banks would not know that they exceeded the $10,000 limit. See id. at 1309-10. Although the defendants had no duty to report the transactions themselves, we upheld their convictions under 18 U.S.C. § 371 because they had “agreed to interfere with and to obstruct this lawful function of the IRS.” Id. at 1313.

Here, the indictment alleges that Shellef and Rubenstein agreed to interfere with the IRS’s collection of the excise tax by conspiring to misrepresent to Allied and Elf the CFC-113’s destination, which in turn would lead them to refrain from paying the excise tax. Just as the Nersesian defendants could be convicted for misrepresenting the nature of their transactions to a third party who owed an independent duty to the IRS, so can Shellef and Ruben-stein.

Shellef seeks to avoid the implications of Nersesian by arguing that “[t]he reason that [the scheme in Nersesian] interfered with the IRS’s lawful function was that the financial institutions could have no way of knowing that [the defendant] was structuring transactions in a way to prevent the banks from submitting” required reports. Shellef Br. at 43. But the ability of the reporting party to discover the true nature of the transaction is related only to the likelihood of the scheme’s success. And, as noted, the likely success of the scheme is immaterial. Giordano, 693 F.2d at 249.

Finally, Shellef argues that the rule of lenity prohibits application of the statute to his conduct. But, as our analysis indicates, the statute, as interpreted by our case law, makes clear that his conduct is proscribed. And “[t]he rule of lenity ... is not applicable unless there is a grievous ambiguity or uncertainty in the language and structure of the [statute], such that even after a court has seized every thing from which aid can be derived, it is still left with an ambiguous statute.” Chapman v. United States, 500 U.S. 453, 463, 111 S.Ct. 1919, 114 L.Ed.2d 524 (1991) (citations, internal brackets, and internal quotation marks omitted).

The indictment sufficiently alleges a violation of 18 U.S.C. § 371.

2. Jury Instructions. Rubenstein asserts that the jury instructions erroneously omitted an essential element from their description of the conspiracy offense. The government responds that, because Ru-benstein made no contemporaneous objection to the instructions, any error was not “plain” as required by our review.

Rubenstein effectively concedes that he did not object to these instructions. But if these instructions were to be issued again in the course of a new trial, Rubenstein presumably would object. Whether any error would be “plain error” is therefore not an issue we need address. We discuss only whether the instructions were erroneous.

The district court instructed the jury on the conspiracy count as follows:

In order to satisfy its burden as to Count One, the government must prove each of the following four essential elements beyond a reasonable doubt: First, that two or more persons entered the unlawful agreement charged in the indictment starting in or about July 1997; second, that each defendant knowingly and willfully became a member of the conspiracy; third, that one of the members of the conspiracy knowingly committed at least one of the overt acts charged in the indictment; and fourth, that the overt act or acts which you find to have been committed was or were committed to further some objective of the conspiracy.

Trial Tr. 3158-59, July 26, 2005.

[W]e have emphasized the need for particular vigilance in enforcing the government’s burden of proof in prosecutions under § 371, in view of the broad range of conduct covered by the federal fraud statutes and the risk that a defendant may be convicted of conspiracy based upon an agreement other than that specifically charged in the government’s indictment.

United States v. Gallerani, 68 F.3d 611, 618 (2d Cir.1995) (internal quotation marks and citation omitted). Applying “particular vigilance,” Gallerani, 68 F.3d at 618, we think that the instruction here was erroneous, see United States v. Bayless, 201 F.3d 116, 127-28 (2d Cir.), cert. denied, 529 U.S. 1061, 120 S.Ct. 1571, 146 L.Ed.2d 474 (2000) (noting that an error exists when there is a “deviation from a legal rule which has not been waived” (internal quotation marks and citation omitted)). The elements of a section 371 conspiracy to defraud the United States are, as we have noted, “(1) [that defendant] entered into an agreement (2) to obstruct a lawful function of the government (3) by deceitful or dishonest means and (4) at least one overt act in furtherance of the conspiracy.” Ballistrea, 101 F.3d at 832 (brackets in' original; citation and internal quotation marks omitted). The district court did not instruct the jurors that they would be required to find that Shellef and Rubenstein agreed to use “deceitful or dishonest means” to obstruct the “lawful function of the government.”

B. Wire Fraud

The government also charged Shellef and Rubenstein with multiple counts of wire fraud. The wire fraud statute makes it a federal crime to use interstate wire communication to execute a “scheme or artifice to defraud, or for obtaining money or property by means of false or fraudulent pretenses, representations, or promises.” 18 U.S.C. § 1343. Shellef and Ru-benstein challenge the sufficiency of the indictment, the sufficiency of the evidence for one of the government’s theories, and the jury instructions.

1. Sufficiency of the Indictment. The indictment here contains two theories of fraud: a “no-sale” theory and a “tax liability” theory. “Where a jury is presented with multiple theories of conviction, one of which is invalid, the jury’s verdict must be overturned if it is impossible to tell which theory formed the basis for conviction.” United States v. Szur, 289 F.3d 200, 208 (2d Cir.2002) (citations omitted).

a. No-Sale Theory

Under the “no-sale” theory, the indictment alleges that Shellefs misrepresentation “induced Allied Signal to sell additional amounts of virgin CFC-113 to Poly Systems that it would not have sold had it known that Shellef in fact intended to sell the product domestically.” Indictment ¶ 53. Shellef contends that this theory is not viable because the scheme did not constitute a scheme to defraud within the meaning of the wire fraud statute. The government responds that Shellef deprived Allied of “ ‘the right to define the terms for the sale of its property’ ” and that this is sufficient to bring his scheme within the reach of the wire fraud statute. Gov’t Br. at 40-43 (quoting United States v. Schwartz, 924 F.2d 410, 421 (2d Cir.1991)).

The “essential elements of a mail or wire fraud violation are (1) a scheme to defraud, (2) money or property as the object of the scheme, and (3) use of the mails or wires to further the scheme.” Fountain v. United States, 357 F.3d 250, 255 (2d Cir.2004), cert. denied, 544 U.S. 1017, 125 S.Ct. 1968, 161 L.Ed.2d 856 (2005) (quotation marks, citation, and brackets omitted). “Because the mail fraud and the wire fraud statutes use the same relevant language, we analyze them the same way.” Schwartz, 924 F.2d at 416. Although the indictment need not allege that the victims of the fraud were in fact injured, it is required to allege that the defendant contemplated actual harm that would befall victims due to his deception in order to meet the “scheme to defraud” prong. See United States v. Novak, 443 F.3d 150, 156 (2d Cir.), cert. de nied, — U.S. -, 127 S.Ct. 525, 166 L.Ed.2d 371 (2006).

Our cases have drawn a fine line between schemes that do no more than cause their victims to enter into transactions they would otherwise avoid-which do not violate the mail or wire fraud statutes — and schemes that depend for their completion on a misrepresentation of an essential element of the bargain — which do violate the mail and wire fraud statutes.

In United States v. Regent Office Supply Co., 421 F.2d 1174 (2d Cir.1970), the defendants sold stationery, id. at 1176. The defendants’ scheme consisted of directing their sales personnel to misrepresent their identities to prospective customers so that the customers would be willing to entertain their offers. See id. (noting, as an example, that the sales personnel fraudulently claimed that they had been referred by a friend of the customer or an officer of the customer’s firm). We concluded that no conviction under the mail fraud statute could stand where the misrepresentation was “not directed to the quality, adequacy or price of goods to be sold, or otherwise to the nature of the bargain.” See id. at 1179.

United States v. Starr, 816 F.2d 94 (2d Cir.1987), is similar. The defendants there collected bulk mailings from their customers and then sent them through the post office. See id. at 95-96. At the post office, however, they hid high-rate mail in low-rate mail packages, and paid the low-rate price for the entire shipments. Id. at 96. The defendants nonetheless charged their customers as if the mailings were high-rate, and produced and mailed false invoices to show that the high-rate price had in fact been paid. Id. We decided that “[t]he misappropriation of funds simply ha[d] no relevance to the object of the contract; namely, the delivery of mail to the appropriate destination in a timely fashion.” Id. at 100. Because “Misrepresentations amounting only to a deceit are insufficient to maintain a mail or wire fraud prosecution,” we concluded that such a charge can not apply to situations where the alleged victims “received exactly what they paid for” and “there was no discrepancy between benefits reasonably anticipated and actual benefits received.” Id. at 98-99 (internal quotation marks and citation omitted); cf. id. at 102 (Newman, J., concurring) (“An indictment for defrauding the Postal Service would have led to a conviction that would surely have been affirmed. However, the indictment for defrauding the customers has led to a conviction that must be reversed.”)

In Schwartz, 924 F.2d 410, however, we were faced with the type of misrepresentation that Regent Office recognized might form the basis for a wire fraud prosecution-that is, one “directed to ... the nature of the bargain,” id. at 1179. The defendants in Schwartz had purchased night-vision goggles from Litton Industries. Schwartz, 924 F.2d at 414. Because the Arms Export Control Act restricted the sale of these goggles to certain nations, Litton sought assurances, both in the contract and during the course of performance, that the defendants would not export to the restricted nations. Id. Though the defendants promised to abide by all applicable export regulations, they sold the goggles to nations that were prohibited from purchasing them. Id. at 414-lb. We upheld their conviction for wire fraud under a no-sale theory because the “misrepresentations went to an essential element of the bargain between the parties and were not simply fraudulent inducements to gain access to' Litton equipment.” Id. at 421. The defendants had “deprived Litton of the right to define the terms for the sale of its property in that way,” that is, that its product not be exported from this country illegally, and therefore “cost it, as well, good will.” Id.

The indictment in the case before us alleges:

It was a further part of the scheme and artifice that by promising to export all of the CFC-113 purchased, defendant DOV SHELLEF induced Allied Signal to sell additional amounts of virgin CFC-113 to Poly Systems that it would not have sold had it known that SHELLEF in fact intended to sell the product domestically-

Indictment ¶ 53. As in Starr, the indictment here does not allege, pursuant to the government’s “no-sale” theory, that there was a “discrepancy between benefits reasonably anticipated” and actual benefits received. Starr, 816 F.2d at 98. And as in Regent Office, it fails to allege that Shellef misrepresented “the nature of the bargain.” Regent Office, 421 F.2d at 1179. Instead, the indictment states only that Shellefs misrepresentation induced Allied to enter into a transaction it would otherwise have avoided. Because it does not assert that Shellefs misrepresentation had “relevance to the object of the contract,” Starr, 816 F.2d at 100, we do not think it is legally sufficient.

We recognize that the facts on which this prosecution rested closely resemble those in Schwartz. As in Schwartz, in the case at bar, government regulations and the contract between the parties called for territorial restrictions on the sale of a product. But we are concerned here only with the sufficiency of the indictment, not the sufficiency of the evidence. The jury here might have erroneously convicted Shellef and Rubenstein even though it concluded that the defendants did not misrepresent an “essential element” of the bargain, but rather made “simpl[e] fraudulent inducements to gain access to” Allied and Elf products. Schwartz, 924 F.2d at 421. Because we cannot rule out that possibility, we do not think a jury can be permitted to convict either defendant on the “no-sale” theory. See Szur, 289 F.3d at 208 (concluding that a remand is required where the jury may have convicted on a legally invalid theory).

b. Tax Liability Theory

Under the “tax liability” theory, the indictment alleges that Shellefs misrepresentation regarding the destination of the CFC-113 “induced Allied Signal to continue to sell the product to Poly Systems without paying the excise tax to the Internal Revenue Service, or including the tax in the price it charged Poly Systems.” Indictment ¶ 52. Shellef argues that the taxes could not have been “property” within the meaning of the wire fraud statute because Shellefs scheme could not have deprived Allied of the tax money that was owed to the federal government.

We disagree. Under the agreement, Shellef owed Allied the amount of “any federal excise tax imposed on the sale of’ the CFC-113 “which is not anticipated by Seller at the time of contract execution.” Allied Contract, effective Jan. 1, 1996, at 4 ¶ ll.C; id. at 2 ¶ 6.B. The agreement also required Shellef to sell the CFC-113 abroad. Id. at 1 ¶ 1. Shellef misrepresented the destination of the CFC-113 he was purchasing from Allied so that he could avoid paying to Allied the price increase necessitated by the application of the excise tax. Allied therefore did not receive the money due it under the agreement, property that was owed to it. To be sure, that money was destined to be passed on to the government. But that is not relevant to our inquiry. Allied had a right to the property and Shellefs scheme was intended to deprive Allied of it. It was therefore a scheme to deprive within the meaning of the wire fraud statute. See United States v. Males, 459 F.3d 154, 158 (2d Cir.2006) (“[I]t is sufficient that a defendant’s scheme was intended to deprive another of property rights, even if the defendant did not physically ‘obtain’ any money or property by taking it from the victim.”).

2. Sufficiency of Evidence. Shellef argues that the evidence was not sufficient to sustain his conviction under the “no-sale” theory. As noted above, we doubt the legal sufficiency of the allegations on the “no-sale” theory and therefore need not and do not consider the evidentiary sufficiency of a conviction based upon it in the previous trial. Shellef does not seriously contest the sufficiency of the evidence at that trial with respect to the “tax liability” theory.

3. Jury Instructions. Ruben-stein asserts that the district court’s instructions as to wire fraud were erroneous because the district court did not caution the jury that Rubenstein could not be found guilty as an aider and abetter based only on a “general knowledge or suspicion that a crime was being committed” or his “ ‘mere association’ with the alleged principal, defendant Shellef.” The district court issued an instruction for the wire fraud counts and included in the instruction a verbatim reading of the aiding and abetting statute. No party appears to contest that they accurately describe the elements of wire fraud. Nor does Rubenstein argue that the aiding and abetting instruction was incorrect-he asserts only that additional cautionary instructions should have been given. We conclude that the instruction was not improper.

C. Evidentiary Rulings

Shellef and Rubenstein assert that evidentiary rulings during the course of trial violated their constitutional right to present a meaningful defense and their Sixth Amendment right to confront witnesses. In light of the deference we owe to a district court’s decisions as to admissibility of evidence, see, e.g., United States v. Ebbers, 458 F.3d 110, 122 (2d Cir.2006), cert. denied, - U.S.-, 127 S.Ct. 1483, 167 L.Ed.2d 244 (2007), and because we cannot foresee what decisions the district court might make in any new trial, or in precisely what context those decisions might be made, we decline to comment on them or the arguments of the government and the defendants in this regard.

CONCLUSION

Having reviewed the remainder of the defendants’ arguments, we conclude that they are without merit. Because the 1996 Tax Counts were improperly joined with the remainder of the charges against Shel-lef and Rubenstein; and because these errors were not harmless, we vacate the judgments of conviction of both defendants and remand the case to the district court for further proceedings. 
      
      . The government dismissed three of the wire fraud counts against Shellef and Rubenstein.
     
      
      . Shellef and Rubenstein each request that we adopt whichever arguments in the other’s brief may be applicable to him. We do so, but for ease of exposition refer individually to the appellant in whose brief a particular argument was made.
     
      
      . At trial, an IRS agent testified that Ruben-stein purchased 21,768 pounds of CFC-113 in 1995. The government, in questioning the witness, referred to Rubenstein's purchase of 201,000 pounds. Our own calculation using the witness's testimony regarding the applicable invoices indicates that Rubenstein purchased 217,812 pounds. We assume that the witness's reference to 21,768 pounds is a transcription error or that the government attorney misspoke.
     
      
      .The record often does not distinguish the acts of Rubenstein from those of his corporations, Stevens and Dunbar. Here, for example, the witnesses testified that Elf credited Rubenstein's account, but the invoices refer to Stevens. Similar confusion exists with respect to Shellef and his various corporate entities. These distinctions are largely irrelevant for our purposes, so we primarily follow the trial transcript. With respect to the tax charges against Shellef, however, the identity of each entity is important and we are therefore precise when we discuss the conduct underlying those charges.
     
      
      . Shellef and Rubenstein sought to persuade the jury that they thought the Elf CFC-113 would also be tax-exempt pursuant to 26 U.S.C. § 4682(d)(1) because it was “reclaimed.” The Elf CFC-113, as shipped by Elf, was blended with alcohol. Shellef, a chemical engineer by training, put the blended material through a water extraction process to separate the CFC-113 from alcohol, thus retaining only pure CFC-113.
     
      
      . Custom placed an order on July 9, 1997, seeking twenty drums of CFC-113 per month for four months. All Discount placed its order on July 11, 1997.
     
      
      . Shellef strenuously contests whether the territorial restrictions on him contained in the original contract remained in effect. On his reading, the Autumn 1998 Agreement did not incorporate the original contract terms limiting sales to the original market. Shellef testified at trial that he believed that, pursuant to the Second Amended Allied Agreement, the limitation to export sales expired on June 30, 1998, and was not revived by the Autumn 1998 Agreement. The Autumn 1998 Agreement made reference to the original contract "as amended,” and the Second Amended Allied Agreement specified that the "terms and conditions of sale[s]” made after June 30, 1998, "shall not be as set forth in the Contract, but shall be negotiated by the parties.” But it also said that Allied "agrees to extend [Shellefs] exclusive rights to sell [CFC-113] in the [Middle East] through the end of 1999.” Allied representatives similarly testified that they understood the new agreement to incorporate the export obligation from the previous agreement.
     
      
      . At trial, evidence was presented to the effect that the re-labeling of materials was a common service rendered at the behest of the product distributor, who did not want the final purchaser to know where the product was manufactured for fear that the purchaser would bypass the distributor and buy the product directly from the manufacturer. Although this practice of “customer protection” might explain the removal of Allied labels, it is unclear why it should also be viewed as necessary for such purposes to change the designation from "virgin” to "reclaimed.” The defendants may have thought that the Elf CFC-113 was "reclaimed,” but there is no evidence that they thought the Allied CFC-113 to be anything but virgin.
     
      
      . "Quicken” is the name given by Intuit Inc. to its widely used group of financial computer programs for consumer and business use. They are used, among other things, to keep financial records, including check registers. See Test, of Stephen Stein, Trial Tr. 1467:12-20, July 6, 2005; Intuit, http://www.intuit. com (last visited July 21, 2007).
     
      
      . This amount is calculated by adding the cash received in a fiscal year to the accounts receivable at the end of that year and then subtracting the accounts receivable that were reported in the prior year and collected in the current year.
     
      
      . We note that Shellef argued in the district court that all the tax charges should be severed from all the non-tax charges but he argues on appeal that the 1996 tax charges were misjoined with the remaining charges, including the 1999 tax charge. The government does not, however, contend that Shel-lef's argument on appeal was waived, and so we consider it as argued and briefed before us.
     
      
      . Indeed, the answer to this question is not well-settled. Compare United States v. Turoff, 853 F.2d 1037, 1043 (2d Cir.1988) (stating that "our cases indicate that when a defendant in a multiple-defendant case challenges joinder of offenses, his motion is made under 8(b) rather than 8(a)”) (internal quotation marks omitted) (citing cases) and Attanasio, 870 F.2d at 814-15 (applying Rule 8(b) to determine whether two conspiracies should have been charged together) with United States v. Biaggi, 909 F.2d 662, 675-76 (2d Cir.1990) (citation omitted) (acknowledging the "thoughtful opinion” of the district court, which limited the reach of Turoff on the ground that it "should be understood to apply Rule 8(b) standards to the claim of a defendant in a multi-defendant trial only when he seeks severance of counts in which he and at least one of his co-defendants are charged,” while leaving open the possibility "that Rule 8(a) standards apply to a defendant in a multi-defendant trial who seeks severance of counts in which he is the only defendant charged,” but failing to resolve the issue because joinder was also proper under Rule 8(b)). We, likewise, need not opine on the reach of Turoff here because our resolution of this appeal is the same even if Rule 8(a), the more expansive joinder provision, applies.
     
      
      . In Biaggi, multiple defendants were involved in a large-scale conspiracy to extort money from a company called Wedtech. See Biaggi, 909 F.2d at 670-74. One defendant was also charged with extorting money from a contractor named Fogliano. See id. at 673. This defendant was further charged with a tax violation for unreported income. See id. at 675. We reasoned that because the overwhelming majority of the unreported income was derived from the Wedtech extortion that was at the center of the trial, joinder was proper notwithstanding that a small amount of the income was from the unrelated Fogli-ano extortion. See id. at 676. Nonetheless, we noted hypothetically that if the trial had focused on the Fogliano extortion, joinder of a tax count based largely on unreported Wed-tech extortion income may be improper, even if it included a small amount of Fogliano extortion income. See id. Biaggi thus reinforced the notion that the propriety of joining tax charges with non-tax charges depends in large part on whether the unreported income forming the basis for the tax charges was derived from the criminal acts that form the basis for the non-tax charges.
      Shellef's case stands even further outside Rule 8’s scope than the hypothetical posed by the Biaggi Court. Here, none of the unreported personal or corporate income was derived from the conspiracy or wire fraud schemes that formed the basis for the other charges against Shellef and Rubenstein. There is simply no meaningful factual overlap between the 1996 Tax Counts and the remainder of the case.
     
      
      . The district court also gave this instruction:
      Any wilful failure to comply with the requirements of the Internal Revenue Code for one year is a separate matter from any such failure to comply for a different year. The tax obligations of defendant Shellef in any one year must be determined separately from the tax obligations in any other year.
      That language is not sufficient to avoid the propensity problem. Even though the jury was instructed to "determined separately” guilt as to the tax charges, this instruction does not explain to the jury that, if it finds Shellef guilty on one tax charge, it may consider this conduct only as it relates to intent to commit the other tax charge. While the instruction properly directs the jury to determine guilt or innocence separately for each count, it does not limit the extent that the jury may consider evidence submitted to prove one count in determining guilt on another count. For the misjoinder to be harmless, given the facts of this case, such an instruction was required.
     
      
      . United States v. Gurary, 860 F.2d 521 (2d Cir.1988), cert. denied, 490 U.S. 1035, 109 S.Ct. 1931, 104 L.Ed.2d 403 (1989), is also analogous. The three defendants in Gurary "sold invoices to corporations ... falsely reflecting that one of the defendants' companies had sold goods to the invoice-purchasing company.” Id. at 523. That it remained for the "[c]orporations purchasing the fictitious invoices [to] include! ] the non-existent goods in their calculations of cost-of-goods sold for tax purposes, fraudulently misstating their taxable income” was ultimately of no moment. See id. (describing scheme); id. at 525 (holding that evidence supported the conspiracy count). Similarly, here, it remained for Allied and Elf to submit documents to the IRS falsely indicating that the CFC-113 they sold to Shellef and Rubenstein was, as they represented, exported. See id. at 525 (noting that "[a]ccurate disclosure of the transactions in corporate records and tax returns would prevent the scheme from working”). But Shellef and Rubenstein cannot avoid guilt by reason of the fact that they did not encourage Allied and Elf to take this further step-the indictment sufficiently alleges that they "were well aware their scheme would ... impede the IRS from learning” the transactions were domestic and hence taxable. Id.
     
      
      . We express no view as to whether this error was harmless. See United States v. Locascio, 6 F.3d 924, 939 (2d Cir.1993), cert. denied, 511 U.S. 1070, 114 S.Ct. 1646, 128 L.Ed.2d 365 (1994) (recognizing that we reverse on the basis of erroneous jury instructions only if "the defendants-appellants can show that the charge given, when read as a whole, caused them prejudice”).
     
      
      . "Whether rooted directly in the Due Process Clause of the Fourteenth Amendment, or in the Compulsory Process or Confrontation clauses of the Sixth Amendment, the Constitution guarantees criminal defendants 'a meaningful opportunity to present a complete defense.' ” Crane v. Kentucky, 476 U.S. 683, 690, 106 S.Ct. 2142, 90 L.Ed.2d 636 (1986) (citations omitted).
     