
    UNITED STATES of America, Appellee, v. David M. DALE, Appellant. UNITED STATES of America, Appellee, v. Michelle ASHTON, Appellant. UNITED STATES of America, Appellee, v. Martin SEGAL, Appellant. UNITED STATES of America, Appellee, v. AUTOMATED DATA MANAGEMENT, INC., Appellant. UNITED STATES of America, Appellee, v. Terence SWEENEY, Appellant.
    Nos. 91-3228 to 91-3232.
    United States Court of Appeals, District of Columbia Circuit.
    Argued Nov. 18, 1992.
    Decided April 6, 1993.
    Rehearing and Rehearing En Banc Denied June 16, 1993.
    
      Samuel J. Buffone, Washington, DC, for appellant David M. Dale in No. 91-3228.
    Paul Mogin, with whom Brendan V. Sullivan, Jr., Washington, DC, was on the brief, for appellant Michelle L. Ashton in No. 91-3229.
    Alan M. Dershowitz, Cambridge, MA, with whom R. Stan Mortenson and Scott L. Nelson, Washington, DC, were on the brief, for appellant Martin Segal in No. 91-3230.
    W. Neil Eggleston, with whom Laura S. Shores, Washington, DC, was on the brief, for appellant Terence A. Sweeney in No. 91-3232.
    Kenneth Michael Robinson, Washington, DC, was on the brief for appellant Automated Data Management, Inc. in No. 91-3231. Robert F. Muse, Boston, MA, also entered an appearance for appellant Automated Data Management, Inc.
    Stephen P. Anthony, Asst. U.S. Atty., with whom Jay B. Stephens, U.S. Atty., and John R. Fisher, Robert J. Meyer and Helene Kazanjian, Asst. U.S. Attys., Washington, DC, were on the brief, for appellee.
    Before WALD, RUTH BADER GINSBURG and HENDERSON, Circuit Judges.
   Opinion PER CURIAM.

PER CURIAM:

The defendants, a corporation and its officers, challenge their convictions and sentences on various counts of fraud against the United States and its agencies. For the reasons set out below, we affirm their convictions in to to but remand for resentencing pursuant to Part X(F) of this opinion.

I. Facts

On appeal from a criminal conviction, this court must view the evidence in the light most favorable to the government, allowing it the benefit of all reasonable inferences that may be drawn from the evidence and permitting the jury to determine the weight and credibility of the evidence. United States v. Smith, 964 F.2d 1221, 1223 (D.C.Cir.1992); United States v. Butler, 924 F.2d 1124, 1126 (D.C.Cir.), cert. denied, — U.S. -, 112 S.Ct. 205, 116 L.Ed.2d 164 (1991). So viewed, the evidence reveals the following material facts.

Defendant Automated Data Management, Inc. (ADM) is a Washington, D.C. firm founded in the early 1980s by defendant Michelle Ashton, its president. In late 1984, Ashton hired defendant David Dale as “Executive Vice-President” and at about the same time issued to him 18% of ADM’s stock, retaining the other 82% for herself. In early 1985, ADM obtained a contract to sell computers to the United States Army under the “minority set-aside” program of the Small Business Administration (SBA).

In late 1985, ADM established offices abroad in Germany and Korea and hired a new vice-president to manage each: defendant Terence Sweeney in Germany and defendant David Bowers in Korea. In addition, defendant Martin Segal was hired as ADM’s in-house accountant in September 1986 and later received the title “Chief Financial Officer.”

In August 1987 Bowers left ADM after a falling-out with Dale and Ashton — and after secretly taping telephone conversations he had with each of them. Bowers subsequently assisted a government investigation of ADM’s operations that led to the defendants’ indictments and convictions. Those convictions were based on the defendants’ allegedly fraudulent tax treatment of various financial transactions involving ADM’s Asian and European operations and on certain alleged misrepresentations or nondisclosures on government forms completed by defendants Ashton and Dale. We now summarize the facts underlying the convictions.

A. Tax Fraud

All five defendants were convicted both of tax fraud and of conspiracy to commit tax fraud. While the substantive tax fraud counts involved only ADM’s 1986 corporate return, the conspiracy count involved other aspects of ADM’s operations in both Asia and Europe. We describe separately the fraudulent activity relating to each location.

1. Asia

After taking charge of ADM’s Korean operations, defendant Bowers determined ADM should take advantage of Asian business opportunities unrelated to its Army contracts. In order to circumvent legal restrictions on such activity, Bowers, after consulting with Dale, arranged for Nancy Edwards, a legal adviser to ADM’s Korean office, to set up a Guam corporation which would not be subject to the restrictions. Edwards and her husband incorporated Asia Management Systems, Inc. in late summer 1986. Soon thereafter the corporate name was changed to ADM Asia and ownership transferred to Ashton, Dale and Bowers. Ashton and Dale each acquired a 37.5% interest in the company, while Bowers received the remaining 25%. Upon Dale’s instruction to acquire additional companies, Bowers arranged for Edwards to purchase four Hong Kong corporations, Capulus, Fossano, Swaffham and Gemona, which were apparently shells with no assets other than documents of incorporation. During late October and early November 1986 ownership of Swaffham and Gemona was transferred to Ashton, Dale and Bowers in the same percentages as ADM Asia. There followed a number of financial transactions involving the related corporations on which the government based some of its tax fraud charges.

First, during 1986 Bowers arranged for Dale and Ashton to obtain payments total-ling $50,000 from ADM funds channelled through the Korean office. Dale received $20,000 in February 1986 and Ashton received $20,000 in May and $10,000 in September. Neither Dale nor Ashton reported these amounts as personal income on their 1986 federal income tax returns.

Second, between August 1986 and March 1987 ADM made three payments to related companies that it treated, falsely, as legitimate business deductions.

In August 1986, ADM paid $200,000 to Arlington Associates (Arlington), a company owned in equal shares by Dale and Ashton. This payment was recorded in Arlington’s books as a bank loan from Guam National Bank. Sometime in late summer or early fall 1986, Dale instructed Bowers to draft documents representing that the $200,000 payment was a loan to Arlington from Asia Management Systems, Inc., the Guam corporation that Ashton, Dale and Bowers had acquired on August 29, 1986, and subsequently renamed ADM Asia, Inc.

During December 1986 ADM paid a total of $417,532 to Swaffham and Gemona, the two Hong Kong companies acquired by Ashton, Dale and Bowers, for studies and services never actually performed. ADM recorded these payments as deductible business expenses.

Finally, in March 1987 Bowers and Dale created a phony debt of $500,000 to Swaff-ham and documentation to support it. The debt was for software development purportedly performed by Swaffham but actually performed by employees of ADM in Korea at a cost of only about $30,000. The debt was treated as an accrual and deducted as a business expense on ADM’s 1986 tax return.

2. Europe

In Germany, defendant Sweeney hired Larry Knight in February 1986 as a consultant to assist with the European operations. Later that same year, Sweeney and Knight formed an interim German partnership to enable ADM to take advantage of non-Army business opportunities in Germany until a German corporation could be established. On November 18, 1986, a German corporation, ADM Hard- und Software Handelgesellschaft GmbH in Deutschland (ADM H & S), was incorporated to assume the partnership’s business. Ownership of ADM H & S was divided among Ashton (87.5%), Dale (37.5%) and Sweeney (25%) and Knight was appointed general manager.

Over the next two years, ADM made substantial payments to Bourbonia Invest AG, a Swiss investment firm operated by Gerd Wormer, an investment counselor and old friend of Knight. At trial, the government asserted and furnished evidence to show that these payments in fact accrued to the benefit of Ashton, Dale, ADM and ADM H & S and were fraudulently treated by ADM as business deductions.

The first Bourbonia payment, for $316,-000, was made in December 1986, pursuant to two invoices signed by Wormer and dated December 11, 1986, a time when Sweeney and Knight were in the midst of a two-day meeting with Wormer at Wormer’s home. One of the invoices sought payment for “Product Development Consulting for the period March 86, to December 86,” Joint Appendix (JA) 1984, and the other “for Services rendered in accordance with letter contract as of March 11, 1986 for Machine Language Translation Research and Development Project,” JA 1985. Request forms to ADM for checks to pay the Bourbonia invoices were marked “OK MS from D. Dale 12/22/86” and “Sent Via Bank Wire 12/22/86” and one of them was signed by Segal. ADM deducted the $316,-000 payment as a business expense on its 1986 tax return. In late 1986, Bourbonia made a payment to ADM H & S of about $125,000 to purchase five vehicles, one for Knight’s use and the other four to be leased to ADM., Inc. Sweeney and Knight characterized the payment as a loan, but the government maintains the funds came from the $316,000 Bourbonia payment and were never intended to be repaid, which in fact they were not.

The second Bourbonia payment was made in January 1988 pursuant to an invoice dated December 26, 1987, requesting payment of $102,655 for “consulting services for 1987 as per sep. agreement.” Ash-ton signed a check request form dated January 5, 1988, indicating payment had been requested by Segal and authorizing payment of the requested amount. Dale signed a check to Bourbonia for $102,655 dated January 26, 1988.

Ashton and Dale both maintained investment accounts with Bourbonia at least as early as 1987. Forms filed with the IRS indicated that in 1987 each had $10,000-$50,000 in an account with Wormer, while in 1988 the balance in each account had grown to more than $100,000.

B. Other Fraudulent Activity

Apart from tax fraud, the jury also convicted Dale, Ashton and ADM of fraud in connection with four forms Dale and Ash-ton submitted to government agencies.

The first three frauds involved forms Dale and Ashton filed with the Department of Defense (DOD) in early 1987 to obtain a security clearance for ADM. In late January and early February 1987, Dale and Ashton each completed a DOD “Personnel Security Questionnaire,” on which each responded “yes” to the question “Do you have any foreign property or business connections or have you ever been employed by or acted as a consultant or representative for a foreign government” and each identified the 87.5% interest held in ADM H & S and ADM Asia. Neither mentioned any connection with Gemona or Swaffham, although each had acquired a 37.5% interest in the two companies by November 1986. In early February 1987 each also completed a DOD “Statement of Full Disclosure of All Foreign Connections,” purporting to “hereby explain and fully disclose my foreign connections” but listing only their interests in ADM H & S. Finally, about the same time, Ashton signed a DOD “Certificate Pertaining to Foreign Interests” in which she responded “no” to the question “Does your organization have interlocking directors with foreign interests.” Dale also signed the document to certify that Ashton had authority to act on ADM’s behalf.

The fourth fraud related to an “Application for Small Business Determination” Ashton filed with the Small Business Administration (SBA) on April 10, 1987. On the form she identified herself and Dale as officers of ADM and answered “yes” to the question “Are any of the persons listed [above as owners, partners, officers, directors, & principal stockholders] owners, partners, directors, officers, employees or principal stockholders in any other company?” In response to a direction to identify the other companies and offices held, however, she failed to mention her or Dale’s interests in or positions with Arlington, Swaffham, Gemona, ADM, ADM H & S or ADM Asia.

C. Bowers’ Disaffection and Its Aftermath

According to Bowers, in early 1987 he became concerned about his future with ADM and about potential criminal liability. As a result, he took a number of measures in contemplation of departing ADM. . First, in March 1987, he began to tape record telephone conversations he had with both Ashton and Dale, in an apparent effort to protect himself. Next, in April1987 Bowers withdrew about $100,000 from Gemo-na’s and Swaffham’s bank accounts, reasoning that the funds represented his 25% interest in the two corporations. Later, sometime after mid-July, he withdrew the remaining money from the corporations’ accounts, again, according to his testimony, to protect himself. Finally, on August 14, 1987, Bowers faxed a resignation letter to Ashton in the United States.

In response to Bowers’ resignation, Ash-ton and Segal flew to Korea and negotiations ensued during which Ashton, through Segal, attempted to persuade Bowers to turn over all business records, including all tape recordings of telephone conversations, to surrender his interests in ADM Asia, Gemona and Swaffham and to agree to several measures designed to protect the interests of ADM, Dale and Ashton. Ultimately, Bowers returned to the United States, without succumbing to Ashton’s demands, and sought legal counsel.

After Bowers’ resignation ADM and its principals took steps to alter the tax treatment of many of the transactions described above.

First, sometime in August or September 1987, Segal informed ADM’s outside accountant, Grant Thornton, that ADM’s records had to be changed because of recently discovered information, namely that the $417,532 paid to Gemona and Swaffham in December 1986, allegedly for marketing studies, was not deductible and that there were additional Korean revenue of $348,-337 that had not previously been “booked.” The accountants accordingly prepared ADM’s 1986 tax return, which, pursuant to an extension, was not filed until September 15. 1987, to reflect this information. An amended return, filed in 1988, reduced the amount of the additional revenue to $311,-643.

Second, on November 30, 1987, Dale and Ashton met with their personal accountant and told him they had received expense advances in 1986 that had not been included on their 1986 individual returns. After this meeting, Ashton filed an amended 1986 tax return dated December 2, 1987, adding to her taxable income $40,000 that she characterized as “travel advances not included in her 1986 W-2 wages.” JA 2217-18. Dale decided against filing an amended return because he wanted to determine whether his extra $10,000 might be offset by amounts ADM owed him. He subsequently added the $10,000 to the taxable income reported in his 1987 tax return.

Third, at some point, probably after August 21, 1987, Dale and Ashton signed a promissory note to repay ADM the $200,-000 it had furnished to Arlington in August 1986. The payment to Arlington had initially been recorded as a loan from Guam National Bank and was later characterized by Dale as a loan from Asia Management Systems, Inc. This note is now marked “paid 12/31/87.” JA 1979.

Fourth, at some point, apparently during summer 1988 after federal agents searched ADM’s headquarters on June 16, 1988, Se-gal informed one of ADM’s accountants that in December 1986 ADM had mistakenly paid $316,000 in consulting fees on behalf of ADM H & S and asked what should be done. The accountant then prepared an amended 1986 return, dated August 25, 1988, and signed by Ashton, eliminating the deduction previously taken for the December 1986 Bourbonia payment. In a memorandum to the accountant dated August 8, 1988, Segal explained that both that payment and the $102,655 payment in the following year “were paid in error by ADM, Inc.” JA 2349. The memo further stated that “a loan will be set up in Michelle’s and David’s name to ADM, Inc. for the amounts sent to Bourbonia” and that “[¡Interest on the notes will accrue from the day the funds were disbursed from ADM, Inc.” Id. Subsequently, four promissory notes were prepared, dated August 10, 1988, dividing the indebtedness between Dale and Ashton according to their respective ownership interests in ADM. Ashton and Dale each signed two of the notes and Segal witnessed all four. Each note is now marked “Paid 8/12/88.” See JA 2034, 2035.

Finally, in March 1989, after additional government investigation and subpoenaing of documents, Segal told one of ADM’s accountants that he had discovered a $500,-000 accrual taken as a deduction in 1986 that had not been reversed when it later went unpaid. Accordingly, the accountant prepared an amended return, dated March 30, 1989, deleting the $500,000 deduction, and Segal signed it. The amended return explained its purpose as “[t]o adjust consulting expense for amounts accrued in 1986 but never paid subsequent December 31, 1986 [sic] and erroneously not reversed by Accounting Department.” JA 2253.

D. Indictment and Trial

On January 11, 1990, an indictment was returned against ADM, Dale, Ashton, Sweeney and Segal, charging the following counts:

(1) Against all five defendants: conspiracy (in violation of 18 U.S.C. § 371) (a) to defraud the United States by impeding the IRS’ assessment and collection of taxes and (b) to commit the following offenses against the United States: (i) tax evasion (26 U.S.C. § 7201), (ii) subscribing to a false return and aiding and abetting the preparation of a false return (26 U.S.C. §§ 7206(1) and 7206(2)) and (iii) false statements and concealing facts by trick, scheme and device from the IRS, the SBA and the DOD (18 U.S.C. § 1001);
(2) Against Dale and ADM: subscribing to a false tax return (in violation of 26 U.S.C. § 7206(1)) (for signing the 1986 ADM tax return falsely deducting the $500,0000 debt to Swaffham and the $316,000 payment to Bourbonia);
(3) Against Ashton, Sweeney and Se-gal: aiding and assisting in the preparation and presentation of a false and fraudulent return (in violation of 26 U.S.C. § 7206(2)) (for actions related to ADM’s 1986 return and its two fraudulent deductions);
(4) Against all five defendants: attempted tax evasion (in violation of 26 U.S.C. § 7201) and aiding and abetting (in violation of 18 U.S.C. § 2) (for actions related to the underreporting of taxable income on ADM’s 1986 return);
(5) Against Dale, Ashton, Sweeney and ADM: wire fraud (in violation of 18 U.S.C. § 1343) and aiding and abetting (in violation of 18 U.S.C. § 2) (for causing the wire transfer of the $316,000 Bourbo-nia payment with intent to commit tax fraud);
(6) Against Ashton and ADM: concealing facts by trick, scheme and artifice (in violation of 18 U.S.C. § 1001) and aiding and abetting (in violation of 18 U.S.C. § 2) (for Ashton’s nondisclosure of her relationship with Gemona or Swaffham in the DOD “Personnel Security Questionnaire”);
(7) Against Dale and ADM: concealing facts by trick, scheme and artifice (in violation of 18 U.S.C. § 1001) and aiding and abetting (in violation of 18 U.S.C. § 2) (for the same nondisclosure in Dale’s “Personnel Security Questionnaire”);
(8) Against Ashton and ADM: concealing facts by trick, scheme and artifice (in violation of 18 U.S.C. § 1001) and aiding and abetting (in violation of 18 U.S.C. § 2) (for Ashton’s nondisclosure of her Swaffham and Gemona interests in her February 1987 “Statement of Full Disclosure of All Foreign Connections”);
(9) Against Dale and ADM: concealing facts by trick, scheme and artifice (in violation of 18 U.S.C. § 1001) and aiding and abetting (in violation of 18 U.S.C. § 2) (for Dale’s identical nondisclosure); and
(10) Against Dale, Ashton and ADM: making false statements (in violation of 18 U.S.C. § 1001) and aiding and abetting (in violation of 18 U.S.C. § 2) (for denying the existence of interlocking directorships with foreign interests in the “Certificate Pertaining to Foreign Interests”).

JA 141-74.

On July 23, 1990, after a lengthy trial, a jury returned a guilty verdict on each count against each defendant named therein. On July 15, 1991, the trial court sentenced Dale, Ashton, Segal and ADM. Dale was sentenced to 41 months’ imprisonment on count 1, with concurrent 30 month sentences on each of the other counts against him, 2 years’ supervised release, a special assessment of $350 and a $675,000 fine and was assessed $58,037.96 for incarceration costs. Ashton was sentenced to 37 months’ imprisonment on count 1, with concurrent 30 month sentences on each of the other counts against her, 2 years’ supervised release and a $225,000 fine and was assessed $52,375.72 for incarceration costs. Segal was sentenced to 24 months’ imprisonment on count 1, with concurrent sentences of 12 months on each of the other counts against him. ' ADM was assessed a $360,000 fine and a $450 special assessment. Sweeney’s sentencing was delayed until August 13, 1991, when he was sentenced to concurrent prison terms of 18 months on counts 1, 3, 4 and 5, 2 years of supervised release and a $15,000 fine. The defendants challenge both their convictions and sentences and we address their various arguments below.

II. Sufficiency of the Evidence

Each defendant challenges the sufficiency of the evidence to support the convictions. The court’s review here is a narrow one. First, as noted above, we must view the evidence in the light most favorable to the government, deferring to the jury’s weight and credibility determinations. United States v. Smith, 964 F.2d 1221, 1222 (D.C.Cir.1992); United States v. Butler, 924 F.2d 1124, 1126 (D.C.Cir.), cert. denied, — U.S. -, 112 S.Ct. 205, 116 L.Ed.2d 164 (1991). In addition, the court must affirm each conviction if any rational trier of fact could have found the essential elements of the offense charged beyond a reasonable doubt. United States v. Long, 905 F.2d 1572, 1576 (D.C.Cir.), cert. denied, 498 U.S. 948, 111 S.Ct. 365, 112 L.Ed.2d 328 (1990). Applying these principles, we reject seriatim each defendant’s sufficiency challenge.

A. Ashton

Defendant Ashton contends there was insufficient evidence to support her conviction on any of the counts on which she was convicted, namely counts 1, 3, 4, 5, 6, 8 and 10. For the following reasons, we find the evidence sufficient to support her convictions on all seven counts.

First, Ashton argues we must reverse her convictions on counts 6, 8 and 10, charging her with concealing facts from and making false statements to the federal government in violation of 18 U.S.C. § 1001 and those portions of count 1 alleging conspiracy to violate that section because the evidence was insufficient to establish either that her misstatements or nondisclosures on the DOD and SBA forms were made “knowingly and willfully,” as required under the statute, or that they were material. We find neither contention persuasive.

Ashton’s first challenge to her convictions on counts 6, 8 and 10 is that under a reasonable interpretation of the forms cited in those counts, her statements on them were literally true and complete. While Ashton’s interpretation of the law regarding section 1001 appears consistent with the holdings in other circuits, we nevertheless conclude her convictions must be affirmed because, her statements on those forms were not literally true under a reasonable interpretation of the forms.

Ashton first claims she could not be convicted under counts 6 and 8 because the expressions “foreign ... business connections” in the “Personnel Security Questionnaire” (count 6) and “foreign connections” in the “Statement of Full Disclosure of All Foreign Connections” (count 8) can reasonably be interpreted to refer only to “actual status as an owner or director of a foreign company,” and that she did not enjoy that status when she completed those forms because certain formalities required under Hong Kong law had not yet been satisfied. We reject this claim summarily, finding Ashton’s interpretation of “connections” far too restrictive. In its common usage, the word “connection” has a broad meaning that certainly embraces Ash-ton’s relationship to the two Hong Kong corporations of which she was by January 1987 indisputably both an owner and director, if not de jure at least de facto. Because Ashton’s proffered construction of the forms’ language was unreasonable, we reject her challenge to her convictions on counts 6 and 8.

We similarly reject Ashton’s challenge to count 10. Ashton contends her denial on the 1987 “Certificate Pertaining to Foreign Interests” that ADM had “interlocking directors with foreign interests” was literally true because foreign interests can reasonably be construed to exclude foreign corporations owned by American citizens. We disagree. A “foreign corporation” is clearly a “foreign interest” regardless of ownership, as Ashton herself acknowledged when, on the “Statement of Full Disclosure of all Foreign Connections,” she identified herself as a “Representative of a Foreign Interest” based on her interest in ADM H & S.

Ashton also asserts the count 10 conviction must be reversed because the misrepresentation alleged in that count, the denial of any “foreign interests” in the January 1987 “Certificate Pertaining to Foreign Interests,” was not material. Ash-ton reasons that, because the interlocking directorships between ADM and ADM H & S were discoverable from the February 1987 “Statement of Full Disclosure of All Foreign Connections,” in which she identified ADM H & S as a foreign interest in which she, Dale and Sweeney were directors, it could not have influenced or been material to the DOD. We find this argument also unavailing. Admittedly, in order to give rise to criminal liability under section 1001, a concealment or affirmative misrepresentation must be material. United States v. Hansen, 772 F.2d 940, 949 (D.C.Cir.1985), cert. denied, 475 U.S. 1045, 106 S.Ct. 1262, 89 L.Ed.2d 571 (1986). Nevertheless, even assuming that the earlier disclosure of ADM’s relationship with ADM H & S rendered nondisclosure of that relationship here immaterial, it does not affect Ashton’s liability for failing to disclose the interlocking directorships with Swaffham and Gemona which had not been otherwise disclosed to the DOD and therefore were material.

Ashton’s final sufficiency challenge is that the trial evidence failed to establish that she “willfully” participated in the fraudulent tax deductions alleged in counts 3 and 4, as required under 26 U.S.C. §§ 7206(2) and 7201, or that she had a “conscious knowing intent to defraud” in connection with the wire transfer of funds to Bourbonia alleged in count 5, as required under 18 U.S.C. § 1343, the wire fraud statute. All three of the challenged counts alleged fraud in connection with ADM’s claimed 1986 deductions of the $500,000 Swaffham accrual and the $316,-000 Bourbonia payment. Ashton argues there was no evidence that she was aware the Bourbonia payment was not deductible or that the Swaffham payment was ever made, much less that it was not deductible. We disagree, finding ample evidence to support a finding of the requisite intent.

The evidence against Ashton here is similar in nature and weight to the evidence in United States v. Treadwell, 760 F.2d 327 (D.C.Cir.1985), cert. denied, 474 U.S. 1064, 106 S.Ct. 814, 88 L.Ed.2d 788 (1986), in which this court affirmed the conviction of Treadwell, a real estate firm’s chief executive officer, for conspiring with subordinates to violate federal law even though Treadwell exercised little control over day-to-day operations and claimed to have reimbursed the project and fired one of her subordinates after she learned of the misconduct. The Treadwell court upheld the conviction based on the following circumstantial evidence: (1) Treadwell’s close personal and business relationships with the malfeasant subordinates, (2) her regular meetings with them, (3) her extensive experience “as a government-grant entrepreneur” and (4) her attempt to conceal the misconduct by altering and destroying documents. Id. at 333-35. The court concluded: “Combining these factors with the sheer magnitude of the [illegal acts], many involving other businesses that she controlled, would fully support a reasonable inference that Treadwell knew of and condoned her subordinates’ malfeasance.” Id. at 335. Similar evidence here, when viewed most favorably to the government, supports Ashton’s conviction.

The record yields the following facts to support the finding that Ashton willingly participated in the frauds alleged: (1) she was the majority shareholder in all of the corporations; (2) she took an active role in the corporations, signing authorizations and travelling to the foreign offices; (3) the frauds conferred a financial benefit on ADM, Swaffham and ADM H & S, in which she owned controlling interests, as well as on her personal Bourbonia investment account; (4) these transactions were part of a much larger scheme to defraud the government, which included Ashton’s personal withdrawals of ADM funds which she failed to report as income and misrepresentations to government agencies; (5) one of her other misrepresentations was the concealment of the existence of Swaffham, one of the corporations benefited by the frauds; and (6) she personally assisted in covering up many of the frauds, including the $316,-000 Bourbonia deduction. As in Tread-well, the combination of these facts suffices to support the jury’s finding that Ashton willfully and intentionally participated in the frauds alleged.

B. Sweeney

Sweeney challenges the sufficiency of the evidence to support his conviction on counts 1, 3, 4 and 5, advancing two arguments: (1) the evidence did not establish that the payments to Bourbonia, or their tax treatment, were fraudulent and (2) assuming there was fraud, the evidence did not support a finding of specific intent on his part to evade taxes. We find neither argument persuasive and conclude the evidence is sufficient to support Sweeney’s conviction on all four counts.

Sweeney first asserts theré was insufficient evidence to establish that the invoices to Bourbonia were in fact fraudulent. We find, however, that the record contains substantial evidence that the invoices were issued for the express purpose of diverting tax-free funds for the benefit of Ashton, Dale and ADM H & S, while conferring a tax benefit on ADM, and that the services identified in them were never intended to be performed.

First, although the December 1986 invoices purported to charge for “Product Development Consulting for the period March 86, to December 86” and “for Services rendered in accordance with the letter contract as of March 11, 1986 for Machine Language Translation Research and Development Project,” JA 1984-85, Knight, who had been a consultant to ADM since February 1986, who had frequently spoken by phone with Wormer during that time, who was the only employee of ADM H & S as of December 1986, and who was meeting with Sweeney and Wormer the entire day of December 11, 1986, the date on the invoices, nevertheless “had no knowledge” that as of December 1986 Wormer had performed $316,000 worth of work for ADM H & S or that ADM had entered any contract with Bourbonia. In addition, despite government subpoenas, no contract with Bour-bonia has ever been produced and Crystal Day, ADM’s “Director of Contracts,” testified that despite a thorough search she was unable to find such a contract and was in fact informed by Sweeney that none existed. Nor was Day able to discover any actual reports from either year, although the 1987 invoices expressly stated that “specific reports were produced or are now underway.” Trial Transcript (Tr.) 2573. In fact, Day herself testified she never heard of Bourbonia before December 1988, although she attended weekly meetings with Ashton, Dale and “mid-level management.” Further, despite Sweeney’s assertion in a February 19, 1988, memorandum that Bourbonia “provides invaluable services to me on virtually a day-to-day basis,” JA 1994, three witnesses who worked in ADM’s German office between 1986 and 1987, namely Lyddi Hudson, Yvonne Burr and Sally Frank, testified they were unaware of any consultation arrangement with Bourbonia, or any Swiss firm, even though Burr had been with the German office since its establishment and the other two women had attended weekly meetings with Sweeney and the other “key players.” Finally, after the federal investigation began, ADM took steps to reverse the initial tax treatment of the $316,000 and $102,655 Bourbonia payments as deductible expenses and Dale and Ashton assumed personal responsibility for repaying both amounts to ADM, signing promissory notes and, according to notations on those notes, paying them off.

Sweeney next asserts that even if the invoices were fraudulent, there is no evidence that he personally knew the fraud was committed for the purpose of tax evasion. In support of his argument, Sweeney relies heavily on the Ninth Circuit’s opinion in United States v. Salerno, 902 F.2d 1429 (9th Cir.1990). We find the reasoning in Salerno inapplicable here.

In Salerno the Ninth Circuit reversed the tax evasion conviction of a former casino manager and his assistant who had embezzled money from the casino through a scheme that made it appear that the missing money had been won by customers, thereby entitling the casino to deduct the stolen amounts on its tax returns. The Salerno court properly found the evidence insufficient because it failed to show the two defendants embezzled the money “not merely for their own benefit but with a specific intent to cause the casino to file false tax returns.” Id. at 1432. In so finding, the court explained:

The government at trial identified no persons other than [the defendants], the cashier and the runner as being involved in the scheme. None of the four individuals was an officer, shareholder, or director of the taxpayer corporation. There was no evidence that any of those individuals had anything to do with the preparation of [the corporation’s] tax returns. There was no evidence linking the embezzlement scheme to any officer, director or shareholder of the taxpayer corporation. There was no evidence that the defendants had any motive for conducting a scheme to defraud the government, or that they ever mentioned their own taxes, much less the tax returns of the casino.

Id. at 1432. In fact, the court concluded: “In this case the filing of the corporate return appears irrelevant to the defendant’s conduct.” Id. at 1433. Not so here. Sweeney was a corporate vice-president who, according to the evidence, may have been promised an equity position. Further, the fraud, as alleged, involved a conspiracy among Sweeney and both principals of the corporation and its only apparent purpose was to obtain unwarranted favorable tax treatment through untaxed disbursements to Ashton, Dale and ADM H & S and unjustified deductions for ADM. Sweeney was certainly in a position to be aware of such a motive and the jury could reasonably have so inferred. Accordingly, we find the evidence, taken as a whole, sufficient to support a finding of specific intent by Sweeney to evade tax liability on ADM’s behalf.

C. Segal

Finally, Segal challenges the sufficiency of the evidence to support his conviction on counts 1, 3 and 4 and, in addition, challenges the trial court’s denial of his motion for a new trial. We reject both challenges, addressing each separately.

First, Segal contends his convictions should be reversed because the evidence was insufficient to establish beyond a reasonable doubt that he knowingly participated in any of the fraudulent activity, asserting he was merely an innocent employee performing the accounting responsibilities his job required. We conclude, however, that the evidence, viewed most favorably to the government, reveals the following facts sufficient to support a finding of knowing participation in the tax frauds: (1) Segal was ADM’s Chief Financial Officer and as such reported directly to Ashton and Dale and attended high-level company meetings with them around the world; (2) Segal failed to disclose to Grant Thornton, ADM’s outside accounting firm, that the suspect transactions with ADM Asia, Gem-ona, Swaffham and ADM H & S were related-party transactions — in fact, he signed a letter to Grant Thornton, dated May 27, 1987, stating, inter alia, that “[rjelated party transactions and related amounts receivable or payable, including sales, purchases, loans, transfers, leasing arrangements and guarantees” had been “properly recorded or disclosed in the financial statements,” JA 2298, while as of that date the $200,000 Arlington payment, the $417,532 payments to Swaffham and Gemona and the $500,000 Swaffham accrual had already occurred but not been identified as related-party transactions; (3) Se-gal knew or should have known that the amount of the $500,000 Swaffham invoice was artificial and that the invoice itself was not bona fide; (4) it was Segal whom Ashton selected to accompany her to Korea in August 1987 and to' negotiate with Bowers, even though it was likely, if not inevitable, that the negotiations would involve discussion of some of the fraudulent activities, as in fact they did; (5) after the Korean sojourn, Segal continued to conceal from Grant Thornton some of the fraudulent tax transactions of which he must have known by then; and (6) in 1988 Segal furnished ADM’s accountants a false explanation of why the 1986 tax return had to be amended to eliminate the deduction of the $316,000 Bourbonia payment. Accordingly, we reject Segal’s first sufficiency challenge.

Next, Segal asserts that even if the evidence was sufficient to support his conviction, the district court nevertheless erred in denying his motion for a new trial on the grounds that the verdict was against the weight of the evidence and that newly discovered evidence, namely testimony given by Sweeney after trial but before sentencing, established Segal’s innocence. A motion for new trial on either of the grounds asserted is committed to the trial court’s sound discretion and may be reversed only for abuse of that discretion. See United States v. Rogers, 918 F.2d 207, 213 (D.C.Cir.1990); United States v. Sensi, 879 F.2d 888, 901 (D.C.Cir.1989). We conclude there was no abuse of discretion here.

First, we find no error in the district court’s denial of the motion insofar as it was based on the weight of the evidence. In considering a new trial motion based on the weight of the evidence the district judge “weighs the evidence and evaluates the witnesses’ credibility and decides whether ‘a serious miscarriage of justice may have occurred.’ ” Rogers, 918 F.2d at 213 (quoting Tibbs v. Florida, 457 U.S. 31, 38 n. 11, 102 S.Ct. 2211, 2216 n. 11, 72 L.Ed.2d 652 (1982)). Our review of the district court’s decision is particularly narrow when the court denies the new trial motion because the court’s decision accords with the jury’s. Hutchinson v. Stuckey, 952 F.2d 1418, 1420 (D.C.Cir.1992) (citing McNeal v. Hi-Lo Powered Scaffolding, Inc., 836 F.2d 637, 646 (D.C.Cir.1988)). Given this limited scope of review and the evidence set out above supporting Segal’s knowing participation in the tax evasion scheme, the trial court’s rejection of Se-gal’s weight of the evidence argument cannot be characterized as an abuse of discretion and must therefore be upheld. See United States v. Kelly, 748 F.2d 691, 701 (D.C.Cir.1984) (holding that, as long as the weight of the evidence clearly weighs in favor of conviction, not against it, there is no abuse of discretion in denying a new trial motion).

Nor do we find error in the judge’s refusal to grant a new trial based on Sweeney’s post-trial testimony. To obtain a new trial based on newly discovered evidence, a convicted defendant must offer evidence that “ ‘ha[s] been discovered since the trial.’ ” Sensi, 879 F.2d at 901 (quoting United States v. Mangieri, 694 F.2d 1270, 1284 (D.C.Cir.1982)). The unanimous view of circuits that have considered the question is that this requirement is not met simply by offering the post-trial testimony of a co-conspirator who refused to testify at trial. See United States v. Reyes-Alvarado, 963 F.2d 1184, 1188 (9th Cir.1992) (“ ‘[W]hen a defendant who has chosen not to testify comes forward to offer testimony exculpating a codefendant, the evidence is not “newly discovered.” ’ ”) (quoting United States v. Diggs, 649 F.2d 731, 740 (9th Cir.), cert. denied, 454 U.S. 970, 102 S.Ct. 516, 70 L.Ed.2d 387 (1981)); United States v. Gustafson, 728 F.2d 1078, 1084 (8th Cir.) (finding no abuse of discretion in denying new trial motion based on probability that post-trial testimony of convicted co-defendants, who had agreed to provide government with information in return for lenient sentence, would deviate from their trial testimony and no longer implicate defendant-appellant), cert. denied, 469 U.S. 979, 105 S.Ct. 380, 83 L.Ed.2d 315 (1984); United States v. Metz, 652 F.2d 478, 480 (5th Cir. Unit A Aug. 3, 1981) (rejecting contention that “ ‘newly available’ evidence is synonymous with ‘newly discovered’ evidence” and finding no abuse of discretion in denial of new trial motion based on co-defendant’s post-conviction exculpating affidavits); United States v. Jacobs, 475 F.2d 270, 286 n. 33 (2d Cir.) (“[W]e fully agree with the judge’s alternative ground [for denying a new trial motion], that a court must exercise great caution in considering evidence to be ‘newly discovered’ when it existed all along and was unavailable only because a co-defendant, since convicted, had availed himself of his privilege not to testify.”), cert. denied, 414 U.S. 821, 94 S.Ct. 131, 38 L.Ed.2d 53 (1973). We recently acknowledged this principle in the administrative context to hold that the National Transportation Safety Board had reasonably concluded the proffered testimony of an FAA inspector who had invoked his fifth amendment privilege at a pilot certification hearing but had since pleaded guilty to charges related to the hearing’s subject-matter did not constitute “newly discovered” evidence under an NTSB rule so as to warrant reconsideration of the certification denial. See Chirino v. NTSB, 849 F.2d 1525 (D.C.Cir.1988). In light of our holding in Chirino and the holdings of the other circuits in the cited cases, we conclude it was not an abuse of discretion to deny a new trial based on Sweeney’s post-trial testimony.

III. Admission of Tapes

A. Title III

Title III of the Omnibus Crime Control and Safe Streets Act of 1968, 18 U.S.C. § 2510 et seq., provides, in relevant part, that a person may intercept wire, oral or electronic communications to which the person is a party “unless such communication is intercepted for the purpose of committing any criminal or tortious act in violation of the Constitution or laws of the United States or of any State.” 18 U.S.C. § 2511(2)(d). In their motion to suppress the tape recordings made by Bowers and Roth, the defendants argued that the taping violated Title III because the purpose for taping was to blackmail Dale and Ash-ton for stock and money. The government responded with three independent arguments: (1) Title III does not apply extrater-ritorially and therefore is inapplicable to Bowers' taping in Korea of phone calls to and from the United States; (2) even if Title III applies extraterritorially and Bowers and Roth made the tapes for an illegal purpose, Title III does not mandate suppression where the government is the innocent recipient of tapes made by unindicted co-conspirators in the course of criminal activity; and (3) the defendants failed to meet their burden of proving that Bowers’ or Roth’s primary purpose in taping was either criminal or tortious. The district court did not state explicitly why it denied the motion to suppress, explaining only that it had conducted a three-day evidentia-ry hearing and that “[a]fter careful consideration of the motion, the opposition thereto and the entire record in this case,” the motion should be denied. JA 917. The defendants did not object to the district court’s failure to state its essential findings of fact on the record. See Fed.R.Crim.P. 12(e).

On appeal, the defendants and the government repeated the same arguments regarding suppression of the tapes that they made to the district court. Normally, where the district court denies a motion to suppress but fails to make findings of fact on the record, we may sustain the district court’s decision “if there is any reasonable view of the evidence that will support it.” Scarbeck v. United States, 317 F.2d 546, 562 (D.C.Cir.1962), cert. denied, 374 U.S. 856, 83 S.Ct. 1897, 10 L.Ed.2d 1077 (1963); see also United States v. Mitchell, 951 F.2d 1291, 1299 (D.C.Cir.1991), cert. denied, — U.S. -, 112 S.Ct. 1976, 118 L.Ed.2d 576 (1992); United States v. Caballero, 936 F.2d 1292, 1296 (D.C.Cir.1991), cert. denied, — U.S.-, 112 S.Ct. 943, 117 L.Ed.2d 113 (1992); United States v. Allen, 629 F.2d 51, 57 (D.C.Cir.1980). However, we declined to exercise this option here because we did not know which of three separate legal theories advanced by the government the district court had adopted and what facts, if any, it relied on to support its chosen theory.

By order dated January 8, 1993, we remanded the record to the district court for a clarification of its reasons for admitting the tapes and any relevant factual findings made in support of its admissibility ruling. See United States v. Williams, 951 F.2d 1287, 1290-91 (D.C.Cir.1991) (remand to the district court is appropriate where neither the legal reasoning nor factual findings supporting the denial of a motion to suppress are apparent because it is not clear “[o]ne, that the district court asked the right legal questions in making its ruling; two, that it actually weighed the evidence bearing on the facts needed to answer them”). On January 21, 1993, the district court responded with an order explaining that a memorandum had been prepared subsequent to the court’s denial of the defendants’ motion to suppress the tapes, but while “[i]t was the Court’s understanding that the Memorandum had been filed; it now appears that the Memorandum was not filed. The Memorandum sets forth the reasons the Court ... denied the motion to suppress tapes_ [A] copy of the Memorandum has been signed and is attached as Court Exhibit A.” United States v. Dale, Crim. No. 90-0027, Memorandum Order at 1-2 (D.D.C. Jan. 21, 1993).

In the memorandum, which was filed and made a part of the record, the district court expressly eschewed the first two legal theories pressed by the government, that Title III does not apply extraterritorially or that it does not apply to the government’s innocent receipt of recordings made by a co-conspirator, stating that “[f]or the purpose of this motion, the Court will assume without deciding that Title III applies to all of the tape recordings at issue.” United States v. Dale, Crim. No. 90-0027, Memorandum at 2 n. 1 (D.D.C. Jan. 21, 1993) (“Tapes Memorandum”). Instead, the court found that the evidence supported the government’s third theory and concluded that the “defendants have failed to establish that the motivation for the taping by either Bowers or Roth was criminal or tortious.” Id. at 3. The district court explained that although Bowers

was a willing participant in the illegality in the beginning, there came a time when he became an unwilling participant because he felt that there was a possibility that all of the responsibility for these activities could be placed on him. Bowers stated that he began taping conversations with the defendants at about this time in order to make sure his interests were protected. Specifically, Bowers asserted that with the taping he wanted to make a record which detailed the participation of defendants Ashton and Dale in the criminal activities taking place in Asia and show[ed] that he was receiving directions [from them] as to those activities. It was important to him that it was clear on the recordings that he was not acting alone since he feared that defendants would seek to portray him in that light.

Id. at 5-6. The district court credited this testimony and found that the defendants had not rebutted Bowers’ explanation for the taping. Id. Similarly, the district court found Roth’s explanation that he made the tapes to keep a record of his employment dispute with ADM and not for purposes of extortion to be “entirely credible.” Id. at 4. We permitted the parties to file supplemental briefs addressing these findings, and after reviewing those briefs and the district court’s memorandum, we conclude that the district court’s factual findings were not clearly erroneous.

The burden was on the defendants to prove that Bowers and Roth made the tapes for criminal or tortious purposes, see Traficant v. Commissioner, 884 F.2d 258, 266 (6th Cir.1989); United States v. Phillips, 540 F.2d 319, 326 (8th Cir.), cert. denied, 429 U.S. 1000, 97 S.Ct. 530, 50 L.Ed.2d 611 (1976), and the evidence supports the district court’s conclusion that the defendants failed to meet their burden. In their supplemental brief, the defendants contend that because the district court failed to mention every bit of evidence allegedly probative of Bowers’ and Roth’s intent, the court necessarily overlooked or ignored this evidence. However, the district court was obligated to state only its essential findings on the record, see Fed. R.Crim.P. 12(e), and we do not find that the district court neglected to consider any dis-positive evidence in the record. Indeed, the district court noted that “the evidence presented by defendants to support their claim that Roth conspired with Bowers in a blackmail and extortion plan is scant and unpersuasive,” and further that it “was not persuaded by defendants’ efforts to rebut Bowers’ testimony.” Tapes Memorandum at 4, 6. In any event, simply because the factual record could reasonably lead a fact-finder to conclude that Bowers and Roth did have an illegal or tortious purpose in taping does not mean that the district court’s contrary, and at least equally permissible, view of the facts is clearly erroneous. See Anderson v. Bessemer City, 470 U.S. 564, 574, 105 S.Ct. 1504, 1511-12, 84 L.Ed.2d 518 (1985).

Neither do we find that the district court erred in its legal analysis. Taping phone calls to make an accurate record of a conversation “in order to prevent future distortions by a participant” is not illegal, see United States v. Underhill, 813 F.2d 105, 110 (6th Cir.), cert. denied, 482 U.S. 906, 107 S.Ct. 2484, 96 L.Ed.2d 376 (1987), even when the recording is made in the hopes of producing evidence of an illegal conspiracy, see By-Prod. Corp. v. ArmenBerry Co., 668 F.2d 956, 959-60 (7th Cir.1982). A person may even tape confederates in the hope of obtaining evidence to reduce his own sentence. See United States v. Ruppel, 666 F.2d 261, 271 (5th Cir. Unit A), cert. denied, 458 U.S. 1107, 102 S.Ct. 3487, 73 L.Ed.2d 1369 (1982). Given the district court’s determination that Bowers' purpose for taping was to protect himself and Roth’s purpose was to establish a record of his employment dispute, it would appear that the district court correctly concluded that the tape recordings were not made in violation of Title III. The defendants argue, however, that the district court “may well have applied an erroneous legal standard” by concluding that Title III is not violated where the primary purpose for taping is legal, even though a second, unlawful factor also motivated the taper. Appellants’. Joint Supplemental Brief at 6-7.

The defendants are correct that a violation of Title III is established when “it is shown either (1) that the primary motivation, or (2) that a determinative factor in the actor’s motivation for intercepting the conversation was to commit a criminal, tor-tious, or other injurious act.” See United States v. Vest, 639 F.Supp. 899, 904 (D.Mass.1986), aff'd, 813 F.2d 477 (1st Cir.1987), cert. denied, 488 U.S. 965, 109 S.Ct. 489, 102 L.Ed.2d 526 (1988). Although the district court at one point in the memorandum referred to Roth’s “primary” purpose for taping, Tapes Memorandum at 3, it is clear to us that the district court, which cited Vest, recognized that the defendants were obligated to demonstrate only that some determinative factor in the taping was impermissible. Unfortunately for the defendants, there is no indication that the district court found any of the purposes motivating Bowers and Roth to be illegal. Instead, the court quite clearly stated that “defendants have failed to sustain their burden of proving that Roth acted with an impermissible purpose,” and that “defendants’ argument that Bowers’ motivation behind his taping was illegal or tortious is unconvincing.” Id. at 5-6. In sum, the district court correctly applied the appropriate legal standard in refusing to suppress the tapes.

B. Authentication

The defendants next argue that the district court erred by failing to make an explicit threshold determination that the tapes were trustworthy, especially in light of a defense expert’s report concluding there was a possibility that some tapes had been altered or recorded over. The admission of recordings into evidence is committed to the sound discretion of the trial court, so long as the tapes are authentic, accurate and trustworthy. See United States v. Sandoval, 709 F.2d 1553, 1554 (D.C.Cir.1983); United States v. Slade, 627 F.2d 293, 301 (D.C.Cir.), cert. denied, 449 U.S. 1034, 101 S.Ct. 608, 66 L.Ed.2d 495 (1980); United States v. Haldeman, 559 F.2d 31, 107 (D.C.Cir.1976), cert. denied, 431 U.S. 933, 97 S.Ct. 2641, 53 L.Ed.2d 250 (1977). It was not an abuse of discretion for the district court to admit the tapes into evidence without expressly stating that the tapes were reliable because the record indicates that the court accepted the government’s proffer of trustworthiness and rejected the defendants’ concerns. We believe that in admitting the tapes into evidence, the district court implicitly found that “ ‘the possibilities of misidentification and adulteration [were] eliminated, not absolutely, but as a matter of reasonable probability.’ ” Haldeman, 559 F.2d at 107 (quoting Gass v. United States, 416 F.2d 767, 770 (D.C.Cir.1969)).

To meet its burden of demonstrating the authenticity and accuracy of the tapes, see United States v. King, 587 F.2d 956, 961 (9th Cir.1978), the government first produced IRS Special Agent Kenneth Buck who testified and was cross-examined at length regarding the tapes and in particular, about how the government had inadvertently damaged one part of one tape. Next, Bowers described the mechanism by which he taped telephone conversations, explained the circumstances under which he handed tapes over to government agents and testified that the tapes were fair and accurate recordings of conversations to which he was a party. In addition, the court engaged in a lengthy colloquy with counsel on the accuracy and reliability of the tapes, and the findings of the defense expert regarding potential tampering with the tapes. Finally, the district court gave the defendants the option of having the FBI technician who produced noise-reduced versions of the tapes testify regarding whether the tapes might have been tampered with prior to receipt by the FBI, which offer the defendants declined. Only after all of the foregoing did the district court admit the tapes into evidence and allow them to be played to the jury.

There is no single rigid standard for determining whether a tape recording may be admitted into evidence. See United States v. Lance, 853 F.2d 1177, 1181 (5th Cir.1988) (federal courts do not require “conclusive proof of authenticity” before admitting tapes); Haldeman, 559 F.2d at 107 (evidence of admissibility of tapes “need not conform to any particular model”). Tapes may be authenticated by testimony describing the process or system that created the tape, see United States v. Sivils, 960 F.2d 587, 597 (6th Cir.), cert. denied, — U.S. -, 113 S.Ct. 130, 121 L.Ed.2d 84 (1992); Haldeman, 559 F.2d at 107-09, or by testimony from parties to the conversation affirming that the tape contained an accurate record of what was said. See Lance, 853 F.2d at 1181-82; Sandoval, 709 F.2d at 1555. The district court’s decision to admit the tapes was obviously based on its conclusion that the testimony of both the originator of the tapes and of the IRS agent established the authenticity, accuracy and trustworthiness of the tapes notwithstanding the misgivings of the defendants’ expert. Given the extended discussion of the objections and the government’s evidence in court, we are satisfied that the district court committed no reversible error in failing to make the basis of its ruling explicit.

IV. Admission of Evidence fkom Search

On May 18, 1990, the district court denied, without elaboration, the defendants’ motion to suppress evidence seized in a search of ADM’s offices and warehouse. In responding to our January 8, 1993 request to set forth its reasons for denying the defendants’ motion to suppress the tapes made by Bowers and Roth, the district court has provided this court with a second memorandum, also mistakenly believed by the district court to have been filed in 1990, explaining in detail why the court refused to suppress evidence seized in the search of ADM’s offices. United States v. Dale, Crim. No. 90-0027, Memorandum Order (D.D.C. Jan. 21, 1993) (“Warehouse Memorandum”). In their supplemental briefs,. the parties have addressed the search and suppression issues in light of the district court’s memorandum.

A. Franks Hearing

The defendants argue that the trial court erred in refusing to hold an evidentiary hearing under Franks v. Delaware, 438 U.S. 154, 98 S.Ct. 2674, 57 L.Ed.2d 667 (1978), to investigate alleged defects in the affidavit of Defense Criminal Investigation Service Special Agent Heidi Shintani supporting the warrant to search ADM’s offices and warehouse in Washington, D.C. Although a search warrant is presumptively valid, if the defendant is able to make

a substantial preliminary showing that a false statement knowingly and intentionally, or with reckless disregard for the truth, was included by the affiant in the warrant affidavit, and , if the allegedly false statement is necessary to the finding of probable cause, the Fourth Amendment requires that a hearing be held at the defendant’s request.

Id. at 155-56, 98 S.Ct. at 2676; see United States v. Sobamowo, 892 F.2d 90, 94 (D.C.Cir.1989), cert. denied, 498 U.S. 825, 111 S.Ct. 78, 112 L.Ed.2d 51 (1990). The defendants contend that they made such a showing before the district court by proffering evidence that: allegations in the warrant that ADM illegally substituted products in executing contracts with the Army were false and the affiant Shintani acted with reckless disregard for the truth by failing to investigate the validity of the allegations; the affiant misrepresented the credibility of David Bowers by failing to disclose that Bowers was himself under investigation; and the affiant lied about information provided by former ADM employees. We conclude that the district court properly rejected each of these claims.

First, the defendants produced affidavits from Army officials to establish that ADM had approval from the Army to substitute Magna hard drives for the Wang or Yipcon hard drives originally contracted for. According to the defendants, Agent Shintani’s sole reliance on affidavits from former ADM employees and her failure to contact any Army officials amounted to reckless disregard for the truth. But in general, the failure to investigate fully is not evidence of an affiant’s reckless disregard for the truth. See United States v. Miller, 753 F.2d 1475, 1478 (9th Cir.1985); United States v. Mastroianni, 749 F.2d 900, 909-10 (1st Cir.1984); United States v. Young Buffalo, 591 F.2d 506, 510 (9th Cir.), cert. denied, 441 U.S. 950, 99 S.Ct. 2178, 60 L.Ed.2d 1055 (1979). As the district court explained, probable cause “does not require an officer to exhaust every possible lead, interview all potential witnesses, and accumulate overwhelming corroborative evidence.” Warehouse Memorandum at 18. In fact, Agent Shintani’s failure to contact Army officials may have been entirely prudent given the possibility of a leak back to ADM. According to the affidavit, one informant “indicated that Dale and ADM President Ashton would certainly destroy any incriminating records if they were subpoenaed. She stated Dale would do anything to avoid detection.” JA 258. Rather than evincing a reckless disregard for the truth, the agent’s actions amounted to at most negligence which is insufficient to warrant a Franks hearing. See Franks, 438 U.S. at 171, 98 S.Ct. at 2684.

The defendants next argue that the affiant misrepresented Bowers’ credibility in the affidavit by describing him as a “Confidential Informant” when Bowers was himself under investigation. However, an affiant’s failure to disclose the backgrounds and alleged biases of informants does not establish the affiant's reckless disregard for the truth. See United States v. Wold, 979 F.2d 632, 634 (8th Cir.1992) (failure to disclose that informant had been drug dealer, was cooperating with police in order to receive leniency and was being paid by police did not amount to misrepresentation); United States v. Levasseur, 816 F.2d 37, 43-44 (2d Cir.1987). Moreover, including in the affidavit the fact that Bowers was himself under investigation would not have defeated probable cause because Bowers’ information was corroborated by other informants. According to the district court, “Bowers’ credibility would have been of no moment” to the magistrate since three other informants had corroborated Bowers’ testimony with “independent, consistent, interlocking information.” Warehouse Memorandum at 13; see United States v. Humphreys, 982 F.2d 254, 258-59 (8th Cir.1992) (defendant “fails to understand that, while he may believe that the informants lacked credibility, where the informants’ information is at least partially corroborated, attacks upon credibility and reliability are not crucial to the finding of probable cause”); United States v. Coronel, 750 F.2d 1482 (11th Cir. 1985) (description of informant as “legitimate businessman,” even if recklessly false, did not defeat probable cause which existed apart from informant’s status); United States v. Haimowitz, 706 F.2d

1549, 1556 (11th Cir.1983) (failure to disclose informant’s criminal record did not undermine probable cause where informant’s first-hand information was corroborated by other sources); United States v. Dennis, 625 F.2d 782, 791 (8th Cir.1980).

Finally, the defendants charge that the Shintani affidavit' falsely stated that former employee Margo George had served as an informant because the affidavit of a defense investigator, William Cor-boy, reported George as saying that she had never provided information about ADM to any law enforcement agency. The district court correctly rejected this contention as well. A Franks hearing should be justified by “[ajffidavits or sworn or otherwise reliable statements of witnesses ... or their absence satisfactorily explained.” Franks, 438 U.S. at 171, 98 S.Ct. at 2684. It is problematical whether a defense investigator’s summary of unsworn statements of an informant generally fits the description of “otherwise reliable.” Here the district court reasonably concluded that where the “defendants have not made any attempt to explain the absence of an affidavit from George herself,” an affidavit from an investigator purporting to describe George’s statements to him was insufficient to warrant a Franks hearing. Warehouse Memorandum at 20-21. In addition, given the defendants’ assertion in their motion to suppress that George was “terminated for incompetence” and that she “bore ill will toward” ADM, JA 240, it is not surprising that George might deny to an investigator employed by ADM that she had given information about ADM to a law enforcement agency. Further, the information allegedly provided by George in the affidavit was so precise, including exact locations of particular documents at ADM, that in order for the district court to credit the Corboy declaration, it would have been necessary for the court to conclude that Agent Shintani had herself fabricated much of that specific information.

The Supreme Court has admonished lower courts that affidavits for search warrants

■ must be tested and interpreted by magistrates and courts in a commonsense and realistic fashion. They are normally drafted by nonlawyers in the midst and haste of a criminal investigation. Technical requirements of elaborate specificity once exacted under common law pleadings have no proper place in this area. A grudging or negative attitude by reviewing courts toward warrants will tend to discourage police officers from submitting their evidence to a judicial officer before acting.

United States v. Ventresca, 380 U.S. 102, 108, 85 S.Ct. 741, 746, 13 L.Ed.2d 684 (1965). Against this backdrop, it is apparent that the district court correctly refused to hold a Franks hearing because the defendants failed to make a substantial preliminary showing that the government had knowingly, intentionally or recklessly disregarded the truth.

B. Warrant

The Fourth Amendment prohibition against general warrants requires the government to provide a particular description of the items to be seized. See United States v. Maxwell, 920 F.2d 1028, 1031 (D.C.Cir.1990). In assessing particularity, courts “ ‘are concerned with realities of administration of criminal justice. It is sufficient if the warrant signed by the judicial officer is particular enough if read with reasonable effort by the officer executing the warrant.’ ” United States v. Vaughn, 830 F.2d 1185, 1186 (D.C.Cir.1987) (quoting Moore v. United States, 461 F.2d 1236, 1238 (D.C.Cir.1972)). In this case, the defendants urge that the warrant was not particular enough and therefore that the district court erred in refusing to suppress the evidence seized from ADM’s offices.

The search warrant sought “records and documents as further described in Attachment B.” JA 249. Attachment B in turn stated that the property to be seized consisted of documents which “are believed to contain specific information regarding the false statements and claims made by ADM.” JA 262. More specifically, Attachment B permitted seizure of “business records including, but not limited to,” various categories of documents, such as invoices, receipts and correspondence. Each category was divided in the sentence by semicolons and at the end of the list, followed by a comma, was the phrase “and other records which relate to the criminal scheme outlined in the above affidavit” of Agent Shintani. Finally, the records to be seized were limited to those that “relate to the period June 1, 1984 through the present.” The defendants complain that the warrant was unduly general because some of the items identified (e.g., “internal documents, including agenda and minutes of board of directors meetings”) were too broad, and because the permission to seize records “including, but not limited to” those listed exposed any and all documents to seizure.

The district court found that the warrant was not overly broad because first, the warrant identified specific and limited categories of records to be seized, and second, the warrant limited the search to documents associated with the allegations made in the Shintani affidavit. Warehouse Memorandum at 24-25. We cannot agree with the district court’s first ground for upholding the search. The warrant’s explicit authorization to the. agents to seize “business records including, but not limited to” those specifically identified subjected essentially all of ADM’s records dated after June 1, 1984 to seizure and therefore the warrant, by itself, was not sufficiently particular. See Center Art Galleries-Hawaii, Inc. v. United States, 875 F.2d 747, 749-50 (9th Cir.1989); Rickert v. Sweeney, 813 F.2d 907, 908-09 (8th Cir.1987). However, we concur in the district court’s view that incorporation of Agent Shintani’s affidavit into the warrant provided a sufficient limitation on the government’s search. As we have explained:

[i ]n some circumstances a search warrant may be construed with reference to the affidavit supporting it for purposes of satisfying the particularity requirement. The affidavit may serve this function, however, only if (1) the affidavit accompanies the warrant, and in addition
(2) the warrant uses suitable words of reference which incorporate the affidavit by reference.

Maxwell, 920 F.2d at 1031 (internal quotation omitted).

Taking the second requirement first, the district court expressly found that the search warrant “incorporated by reference the affidavit underlying the search warrant.” Warehouse Memorandum at 3-

4. More specifically, the. court maintained that the “records sought relate to the criminal scheme outlined in the affidavit underlying the search warrant,” and that it .was “clear that ... allegations [in the affidavit], for which the Magistrate found probable cause, were used to refine the scope of the warrant.” Warehouse Memorandum at 25-26. Conversely, the defendants contend that the phrase in the warrant which makes reference to the - affidavit does not limit all the items to be seized but only identifies an additional omnibus category of documents related to the Shintani affidavit which may be seized. We do not accept this interpretation as a fair reading of the warrant as a whole. See Anderson v. Maryland, 427 U.S. 463, 479-82, 96 S.Ct. 2737, 2748-49, 49 L.Ed.2d 627 (1976); United States v. Johnson, 690 F.2d 60, 64 (3d Cir.1982), cert. denied, 459 U.S. 1214, 103 S.Ct. 1212, 75 L.Ed.2d 450 (1983). The phrase “and other records which relate to the criminal scheme outlined in the above affidavit,” is set apart by a comma from the specific categories of documents and therefore appears to modify the entire sentence. Perhaps more importantly, the first two sentences' of Attachment B state:

Based on the information provided by the Confidential Informants and the experience of the affiant, it is believed that the below listed documents are still in ADM’s possession. These documents are believed to contain specific information regarding the false statements and claims made by ADM.

JA 262. Thus, the common-sense reading of the warrant is that the government could seize a variety of specifically identified documents and any other records that related to-the product substitution and tax evasion allegations made in Agent Shinta-ni’s affidavit. We therefore affirm the district court’s decision that the warrant contained “ 'suitable words of reference’ evidencing the magistrate’s explicit intention to incorporate the affidavit.” Maxwell, 920 F.2d at 1032; see also In re Search Warrant, 572 F.2d 321- (D.C.Cir.1977) (warrant which commands executing officers to seize evidence “which facts recited in the accompanying affidavit make out” incorporates the affidavit), cert. denied, 435 U.S. 925, 98 S.Ct. 1491, 55 L.Ed.2d 519 (1978).

While the warrant undoubtedly incorporated the limitations of the affidavit, the record is not clear whether the other requirement, that “the affidavit accompan[y] the warrant,” was literally satisfied. Maxwell, 920 F.2d at 1031; see also United States v. Tagbering, 985 F.2d 946, 948 (8th Cir.1993); Vaughn, 830 F.2d at 1186; cf. Rickert, 813 F.2d at 909 (“An affidavit may provide the necessary particularity for a warrant if it is either incorporated into or attached to the warrant ... [or] is merely present at the search.”). In its memorandum in opposition to the defendants’ motion to suppress, the government stated that “[i]n executing the warrant, the lead agent, Agent Heidi Shintani, had the warrant and affidavit in her possession. As the agents located documents, to the extent they had questions, they consulted her to make sure the documents seized were described in the affidavit.” JA 333. The defendants, on the other hand, argued that the affidavit must not have been “readily available” because ADM representatives did not themselves see the affidavit at the search. JA 244-45 & n. 7. The district court did not resolve this factual dispute in denying the defendants’ motion to suppress. At trial, testimony regarding the use of the affidavit by the executing agents was prohibited by the district court as potentially confusing to the jury since the affidavit involved primarily product substitution charges no longer made against the defendants. However, Agent Shintani explained:

Prior to the search, I had written up a search plan and instructed all the agents to follow specific procedures, and those were to, as they searched a specific location, which we designated beforehand, that they were to collect everything that they were authorized to seize, and identify it as having taken it.
I was the supervisor, I was there to answer questions that any agents had throughout the day.
When we’d find a box with army invoices, which was what we were looking for at the time, we’d look in and see if they had the particular item we were looking for, and if we didn't find them, we'd put them back, so we just took the ones that had what we were specifically looking-for.

Tr. 2694, 2699, 2786. This evidence indicates, at the very least, that Agent Shinta-ni, who prepared the affidavit and obtained the warrant, was present at the search, oversaw the warrant’s execution and guided the participating agents in seizing documents to conform the search to her understanding of the warrant’s requirements. While it is not altogether clear that the affidavit accompanied the warrant at the search, we are satisfied that the precautions taken by the government sufficiently limited the discretion of the executing agents.

In sum, the warrant was not so broad as to rise to the level of a general warrant. Courts may take into consideration the circumstances of the crime in assessing the degree of particularity that should be required of descriptions of items to be seized in the warrant. The Tenth Circuit has written that “[t]he type of criminal activity under investigation in the present case — a drug dealing business — makes it difficult to list with any greater particularity the books and records desired to be seized which evidences such activity.” United States v. Harris, 903 F.2d 770, 775 (10th Cir.1990); see also United States v. Cardwell, 680 F.2d 75, 78 (9th Cir.1982). In the case of product substitution and tax evasion allegations, specificity is even more difficult because evidence of the crimes can be found in almost every type of business document conceivable. Here, we conclude that the warrant was not constitutionally infirm because it identified several specific categories of documents to be seized, incorporated an affidavit to limit the search and was executed by the affiant pursuant to a specific plan.

The defendants argue that even if the warrant was not impermissibly general, the district court erred in refusing to conduct a hearing to determine whether the executing agents in fact complied with the warrant’s limitations. In order to be entitled to such a hearing, the defendants were required to make “factual allegations which, if established, would warrant relief.” United States v. Thornton, 454 F.2d 957, 967 n. 65 (D.C.Cir.1971). The defendants complained to the district court that the length of the search and the volume of the documents seized were excessive, but, as the district court correctly concluded, such assertions were insufficient to establish a ’constitutional violation. Warehouse Memorandum at 26 (citing United States v. Sawyer, 799 F.2d 1494, 1509 (11th Cir.1986), cert. denied, 479 U.S. 1069, 107 S.Ct. 961, 93 L.Ed.2d 1009 (1987)). The defendants failed to allege that the executing agents ignored the warrant’s limitations or to identify to the district court the documents they claimed to have been improperly seized. Warehouse Memorandum at 27-28; see Humphreys, 982 F.2d at 259. Without such allegations, the district court was under no obligation to hold an eviden-tiary hearing on how the search was executed.

V.Wire Fraud

Count 5 charged the defendants with committing “wire fraud,” in violation of 18 U.S.C. § 1343, by wiring $316,000 from a Washington, D.C. bank to Bourbonia’s Swiss account in furtherance of the alleged scheme to defraud the United States of taxes. All defendants argue that their convictions on count 5 must be reversed because the Internal Revenue Code supplies the exclusive basis for tax fraud prosecutions.

The sole decision cited by the parties or found by the court in full support of the defendants’ argument is United States v. Henderson, 386 F.Supp. 1048 (S.D.N.Y.1974) (mail fraud counts dismissed on ground that Congress did not intend application of mail fraud statute to schemes to defraud government of tax revenue) (Wein-feld, J.). While Henderson gives us some pause, we judge it the sounder course to adopt the position and reasoning of all other courts that have published decisions squarely on point. See, e.g., United States v. Condo, 741 F.2d 238, 239 (9th Cir.1984) (per curiam) (mail fraud and § 7206(2) offense), cert. denied, 469 U.S. 1164, 105 S.Ct. 924, 83 L.Ed.2d 936 (1985); United States v. Computer Sciences Corp., 689 F.2d 1181, 1186-88 (4th Cir.1982) (mail fraud plus making false claims to United States Government), cert. denied, 459 U.S. 1105, 103 S.Ct. 729, 74 L.Ed.2d 953 (1983), overruled in nonrelevant part by Busby v. Crown Supply, Inc., 896 F.2d 833, 841 (4th Cir.1990); United States v. Shermetaro, 625 F.2d 104, 109-11 (6th Cir.1980) (conspiracy to defraud United States and tax evasion). Accordingly, we hold that the tax code is not the exclusive regime under which tax fraud schemes may be proseeut-ed and we uphold the wire fraud convictions.

VI.Constructive Amendment of Indictment

All defendants contend that count 1 was constructively amended, impermissibly, to include a separate conspiracy, one to perform acts of concealment after abandonment of the central objectives of the charged conspiracy. “A constructive amendment occurs when the evidence presented at trial and the instructions given to the jury so modify the elements of the offense charged that the defendant may have been convicted on a ground not alleged by the grand jury’s indictment.” United States v. Sayan, 968 F.2d 55, 59-60 (D.C.Cir.1992) (emphasis in original, internal quotations and citations omitted). It suffices to point out that, in this case, the trial judge’s charge closely tracked the language of the indictment. On that ground, and without reaching other infirmities in the defendants’ argument, we judge the defendants’ constructive amendment objection insubstantial.

VII.Sweeney’s Motion for Acquittal

Sweeney contends that his opportunity to defend was prejudicially affected by the failure of the trial judge to rule immediately on the motion to acquit Sweeney made at the close of the government’s case. Because Sweeney invited any oversight that may have occurred, we reject his current plea.

On July 10, 1990, Sweeney filed at the clerk’s office a written Motion for Judgment of Acquittal premised on the government’s alleged failure to prove a prima facie case. Sweeney’s counsel did not state or refer to that motion in court the next day, July 11, when the government rested. On that day, the trial judge inquired of defense counsel:

All right, let me ask counsel, the government has rested, and with respect to a defense case at this point, where do we stand? I mean, am I-I’m not sure the defendants are going to make motions, I’m not sure whether the defendants are ready to go forward this afternoon before the jury, or what?

Tr. 3497. After a short recess, in the presence of Sweeney’s counsel, counsel for ADM advised the court:

I believe I speak on behalf of all the defendants, your honor, it’s the intention of the defendants to rest at this point.

Tr. 3497-98. Sweeney's counsel said nothing of his filed motion for acquittal. Nor did Sweeney’s counsel request a ruling on the motion during the next several days, i.e., the time running from the July 11 close of evidence to the July 19 charge to the jury.

Absent defendant’s consent, it is error for the trial judge to defer ruling on a motion to acquit made at the close of the government’s case. See, e.g., United States v. Neary, 733 F.2d 210, 218-19 (2d Cir.1984); United States v. Rhodes, 631 F.2d 43, 44-45 (5th Cir.1980) (“application of any other rule would penalize a defendant for a trial court’s refusal to issue a ruling at the time clearly required by our previous cases”) (emphasis added); see also Fed.R.Crim.P. 29(a) (governing such motions). A defendant, however, may agree to deferral of a ruling on the motion either expressly or by failing to object. See, e.g., United States v. Dreitzler, 577 F.2d 539, 552 (9th Cir.1978), cert. denied, 440 U.S. 921, 99 S.Ct. 1246, 59 L.Ed.2d 473 (1979); United States v. Brown, 456 F.2d 293, 294 (2d Cir.) (“Absent ... a demand [for an immediate ruling] the situation is treated as if the court had denied the motion.”), cert. denied, 407 U.S. 910, 92 S.Ct. 2436, 32 L.Ed.2d 684 (1972). In this case, “[g]iven [defendant’s] inexplicable failure to correct the [trial] court’s apparent misapprehension” that no motion awaited immediate attention, “[defendant] cannot now complain of a ruling based on that misapprehension.” See United States v. Wider, 951 F.2d 1283, 1287 (D.C.Cir.1991) (affirming trial court’s denial of defense motion for Jencks Act material).

VIII. Conflict of Interest

Sweeney argues that his pretrial counsel’s conflict of interest severely constrained Sweeney’s ability to protect himself against prosecution. The district judge properly refused to address this matter because it was raised far too late.

During the grand jury investigation Sweeney was represented by John Kotelly who was simultaneously representing ADM and Segal. That multiple representation, Sweeney asserts, precluded Kotelly from advising Sweeney to seek immunity from the government in exchange for testimony against his co-defendants. Once indicted, Sweeney promptly engaged new counsel. Not until after the jury returned guilty verdicts did Sweeney complain about Kotelly’s conflict of interests.

Nonjurisdictional objections to the institution of a prosecution, including the conduct of grand jury proceedings, ordinarily are waived unless raised pretrial, although the district court may grant relief from the waiver for good cause shown. See Fed. R.Crim.P. 12(b)(1) & (2), (f); United States v. Madeoy, 912 F.2d 1486, 1490-91 (D.C.Cir.1990), cert. denied, 498 U.S. 1105, 111 S.Ct. 1008, 112 L.Ed.2d 1091 (1991). Sweeney knew of Kotelly’s multiple representation from the start and tendered no cause at all for his long-delayed objection.

IX. Jury Charge Issues

The defendants raise several challenges to the jury charge; none of them warrants upsetting the verdicts.

A. Plain Error

We take up first two instructions the defendants earlier approved: the definition of conspiracy to defraud the United States that the defendants themselves proposed, and an explanation of “deduction” the defendants ultimately accepted, although they preferred a different instruction. When no objection is made before the jury retires, an instruction is reviewed only for “plain error affecting a substantial right so that a miscarriage of justice would otherwise result.” United States v. Lancaster, 968 F.2d 1250, 1254 (D.C.Cir.1992); see also Fed.R.Crim.P. 30, 52(b). In our review we consider “the evidence adduced at trial, the arguments of counsel, ... the content of the entire jury instruction,” and whether, as in this case, the jury had a copy of the indictment during its deliberations. Sayan, 968 F.2d at 60 (quoting United States v. Chan Chun-Yin, 958 F.2d 440, 444 (D.C.Cir.), cert. denied, — U.S.-, 112 S.Ct. 3010, 120 L.Ed.2d 884 (1992)). This court is “especially reluctant to reverse for plain error when it is ‘invited.’ ” United States v. Mangieri, 694 F.2d 1270, 1280 (D.C.Cir.1982).

B. Conspiracy to Defraud the United States

The district court described the alleged conspiracy to defraud as an agreement “to defraud the United States by impeding, impairing, obstructing and defeating the lawful functions of the Internal Revenue Service in the ascertainment, computation, assessment and collection of income taxes.” Tr. 4517; see also id. at 4516 (court read to jury portion of indictment containing same definition). The defendants argue that this instruction contains terms in need of more precise definition, all the more so because the government’s admission that the defendants had actually paid all the taxes due “narrowed the conspiracy,” leaving its purpose obscure. Dale Brief at 31.

The defendants isolate an instruction that is properly read in context. The district judge read portions of the indictment to the jury as part of its instructions and gave an adequately detailed explanation of the law of conspiracy taken from the standard District of Columbia jury instructions. The charge was at least as informing as the one we upheld in United States v. Treadwell, 760 F.2d 327, 337 & n. 16 (D.C.Cir.1985), cert. denied, 474 U.S. 1064, 106 S.Ct. 814, 88 L.Ed.2d 788 (1986).

The defendants nevertheless urge that the imprecision of the conspiracy to defraud definition left the jury free to convict on the misguided notion that lawful conduct, in particular, the filing of an amended return, could demonstrate the requisite disturbance of a governmental process. This implausible argument again omits consideration of the charge as a whole. The trial court’s .instructions made it clear that a conspiracy to defraud the United States required willful action with specific intent to deceive or cheat. On the point of special concern to the defendants, the district judge instructed later in his charge that “[t]he government encourages [the] use [of amended returns] as a means of correcting mistakes. ' Therefore, the filing of an amended return is not necessarily evidence of intentional misconduct in the filing of the original return.” Tr. 4548. We note, in addition, that the government’s closing argument focused on the knowledge and specific intent of each defendant. See Chan Chun-Yin, 958 F.2d at 444 (consider-, ing government’s closing statement in plain error measurement of jury charge). In sum, no plain error infected the district court’s explanation of the offense of conspiracy to defraud the United States.

C. Deductible Expenses

On deductible expenses, the defense originally requested this instruction:

The issue for you to decide is whether the Government has proven beyond a reasonable doubt that the $500,000 accrual for software development costs and the $316,000 paid to Bourbonia did not represent ordinary and necessary expenses of ADM’s business.
An ordinary and necessary' expense is one that is appropriate and helpful to the conduct of the taxpayer’s business. For example, the costs of software development and marketing studies would normally be deductible expenses for a company like ADM that is in the business of selling software and related products.

ADM Brief at 32. Instead, on agreement of all counsel, the trial judge gave a much shorter instruction defining “deduction”:

The term “deduction” means any item allowed by the internal revenue laws to be subtracted from gross income in computing the amount of taxable income for income tax purposes.

Tr. 4547.

The defendants argue that the abbreviated instruction, and the failure to give the originally requested instruction, left it open to the jury to convict simply upon finding that documents supporting claimed deductions were false. This matter, however, was addressed earlier in the instructions. The district judge charged

[a]s to both counts 2 and 3, you are further instructed that if a person in good faith believes that an income tax return truthfully reports the taxable income and allowable deductions of the taxpayer ... he or she cannot be guilty.

Tr. 4534. Similarly, the judge charged on count 4 that “if a person in good faith believes that he has paid all the taxes that he owes, he cannot be guilty.” Tr. 4537. The absence from the charge of a deductible expense definition of the kind proposed by the defendants, in this light, was not error, and surely not plain error.

D. Truth as Defense

Ashton, ADM, and Dale assert error in the trial court’s refusal to give an instruction on truth as a defense to the charge of violating 28 U.S.C. § 1001. Counsel proposed the truth-as-a-defense instruction for the first time after closing arguments and final jury instructions. The district judge committed no reversible error by failing to supplement his charge, for “the substance of [the defense] theory was conveyed in the jury instructions as a whole.” Sayan, 968 F.2d at 63 & n. 9 (citing United States v. Tarantino, 846 F.2d 1384, 1400 (D.C.Cir.), cert. denied, 488 U.S. 867, 109 S.Ct. 174, 102 L.Ed.2d 143 (1988)); see also United States v. GAF Corp., 928 F.2d 1253, 1263 (2d Cir.1991) (no duty to marshal evidence).

The supplemental charge the defendants requested read:

With respect to counts 6 through 10, if you find that the Defense Department forms allegedly filled out by the defendants Dale, Ashton[,] and Automated Data Management were, in fact, true when made by defendants Dale, Ash-ton[,] and Automated Data Management, you must find these defendants not guilty of the specific counts.

Tr. 4570. The proposed charge was designed to highlight the defendants’ argument, discussed above in connection with the sufficiency of the evidence, that Dale and Ashton may not have qualified as legal owners of Hong Kong companies Swaff-ham and Gemona at the relevant time. (The transfer documents, the defendants had emphasized, remained to be stamped.)

The instructions included in the charge, as the district court observed to counsel, captured the correct proposition that full and truthful disclosure would require acquittal on counts 6 through 10. See Tr. 4565, 4567, 4568. On counts 6 through 9 the court explained that “a trick, scheme or device” necessitated inter alia nondisclosure of a “fact.” Tr. 4543-44. Similarly on count 10, the judge charged the jury that the government was required to prove, inter alia, “that the defendant made a false statement or made a false writing or document in relation to a matter within the jurisdiction of the Department of Defense.” Tr. 4545. The judge also instructed that “[t]he prosecution has the burden of proving beyond a reasonable doubt that the defendant ... knowingly and willfully made a false statement.” Tr. 4546. We discern no fatal omission or infirmity in these instructions.

E. Reasonable Doubt

Over the objections of all defendants, the trial judge used the standard “Red Book” definition of reasonable doubt:

Reasonable doubt, as that name implies, is a doubt based on reason, it is a doubt for which you can give a reason. It is such a doubt as would cause a juror, after careful and candid and impartial consideration of all the evidence, to be so undecided that he cannot say that he has an abiding conviction of the defendant's guilt. It is such a doubt as would cause a reasonable person to hesitate or to pause in the graver or more important transactions of life. However, it is not a fanciful doubt, nor a whimsical doubt, nor a doubt based on conjecture. It is a doubt that is based on reason. The government is not required to establish guilt beyond all doubt or to a mathematical certainty or to a scientific certainty. The government’s burden is to establish guilt beyond a reasonable doubt.

Tr. 4506-07 (emphasis added to phrases defendants contest). The defendants argue that the words “a doubt for which you can give a reason” imply that a juror must be able to articulate a reason; such a requirement, the defendants urge, imper-missibly lowers the government's persuasion burden. ADM Brief at 36-37; see Cage v. Louisiana, 498 U.S. 39, 40-41, 111 S.Ct. 328, 329-30, 112 L.Ed.2d 339 (1990) (disapproving inclusion in “reasonable doubt” charge of definitional words: “such doubt as would give rise to a grave uncertainty,” “an actual substantial doubt,” “a moral certainty”); Perez v. Irwin, 963 F.2d 499, 502 (2d Cir.1992) (disapproving definition of “reasonable doubt” as “doubt to a moral certainty”). The defendants consider the words “so undecided” to exacerbate the problem by conveying the impression that a high degree of indecision is needed in order to find a defendant not guilty. See ADM Brief at 38 n. 49.

We are satisfied that, “in the context of the instructions as a whole and the trial record,” there is no “reasonable likelihood that the jury ... applied the challenged instruction in a way that violates the Constitution.” See Estelle v. McGuire, — U.S. -, -, 112 S.Ct. 475, 482, 116 L.Ed.2d 385 (1991) (citations and internal quotations omitted). The instruction in its entirety fairly conveyed that the requisite doubt must be “based on reason” as distinguished from fancy, whim or conjecture. Cf. Cage, 498 U.S. at 40, 111 S.Ct. at 329 (Court did not find offensive instruction that “a reasonable doubt” is one “founded upon a real tangible substantial basis and not upon mere caprice and conjecture”).

X. Sentencing Issues

A. Straddle Offenses

The defendants argue that the trial court erred in sentencing them on count 1 under the Sentencing Guidelines (“Guidelines”) because: (1) the Guidelines should not apply unless every element of the offense is satisfied by conduct occurring after the Guidelines took effect on November 1, 1987; (2) the false statements purpose of the conspiracy was completed by November 1, 1987, and since the jury’s verdict did not specify whether the purpose of the conspiracy was to make false statements or to evade taxes it is unclear whether the jury found that the conspiracy continued after November 1, 1987; or (3) the jury did not explicitly find that each defendant continued to be involved in the conspiracy after that date. We reject each of these arguments.

First, we agree with every circuit which has addressed the issue that the Guidelines apply to offenses that begin before November 1, 1987, and continue after that date. See United States v. Thomas, 895 F.2d 51, 57 (1st Cir.1990); United States v. Underwood, 932 F.2d 1049, 1053-55 (2d Cir.), cert. denied, — U.S.-, 112 S.Ct. 382, 116 L.Ed.2d 333 (1991); United States v. Rosa, 891 F.2d 1063, 1069 (3d Cir.1989); United States v. Engleman, 916 F.2d 182, 185 (4th Cir.1990); United States v. Van Nymegen, 910 F.2d 164, 166 (5th Cir.1990); United States v. Sloman, 909 F.2d 176, 182-83 (6th Cir.1990); United States v. McKenzie, 922 F.2d 1323, 1328 (7th Cir.), cert. denied, - U.S.-, 112 S.Ct. 163, 116 L.Ed.2d 127 (1991); United States v. Tharp, 892 F.2d 691, 693-95 (8th Cir.1989); United States v. Kohl, 972 F.2d 294, 297-98 (9th Cir.1992); United States v. Williams, 897 F.2d 1034, 1040 (10th Cir.1990), cert. denied, - U.S.-, 111 S.Ct. 2064, 114 L.Ed.2d 469 (1991); United States v. Terzado-Madruga, 897 F.2d 1099 (11th Cir.1990).

Second, although the jury’s general verdict did not specify whether the purpose of the conspiracy was to make false statements or to evade taxes, the district court itself determined that both objects of the conspiracy continued after November 1, 1987. Since the timing of the conspiracy in this regard implicates sentencing only, the district court was entitled to make a factual determination on its duration under a preponderance of the evidence standard. See Underwood, 932 F.2d at 1055. In their Memorandum Concerning the Non-Applicability of the Sentencing Guidelines, the defendants argued to the district court that, “the general verdicts of guilty on Count One clearly do not establish that defendants participated in a conspiracy continuing beyond November 1, 1987.” However, the court responded in an order: “After giving careful consideration to the defendants’ objection to the applicability of the Sentencing Guidelines to Count 1 of the indictment the Court concludes that the Guidelines apply to that Count_” JA 1772. The district court also subsequently adopted the factual findings of the defendants’ presentence reports, which described both objects of the conspiracy as continuing after November 1, 1987. Since the factual basis for the district court’s decision that the Guidelines should apply to the conspiracy count is not clearly erroneous, we affirm. Underwood, 932 F.2d at 1055.

Third, the jury was not required to find that each of the defendants continued to participate in the conspiracy after November 1, 1987. Instead, the defendants had the burden of proving that they affirmatively withdrew from the conspiracy before that date, and because they failed to do so, the Guidelines were properly applied to them. See United States v. Hirschfeld, 964 F.2d 318, 323-24 (4th Cir.1992), cert. denied, - U.S.-, 113 S.Ct. 1067, 122 L.Ed.2d 371 (1993); Williams, 897 F.2d at 1040; United States v. Watford, 894 F.2d 665, 670-71 (4th Cir.1990); Rosa, 891 F.2d at 1069.

B. Base Offense Level

The trial court assigned the defendants Ashton and Dale a base offense level of 16 under §§ 2T1.1 and 2T4.1 of the Guidelines, the level for a conspiracy to evade taxes with a tax loss of between $1,000,001 and $2,000,000. To reach this base offense level, the district court first treated the different objects of the conspiracy as separate counts of conviction pursuant to § 1B1.2, which provides that “[a] conviction on a count charging a conspiracy to commit more than one offense shall be treated as if the defendant had been convicted on a separate count of conspiracy for each offense that the defendant conspired to commit.” Next, under § 3D1.2, the district court combined the object offenses “into a single Group,” such that instead of sentencing the defendants for each object offense, the court would sentence the defendants on the basis of only one of the offenses. Finally, according to § 3D1.3, which states that “the offense level applicable to a Group is the offense level ... for the most serious of the counts comprising the Group, i.e., the highest offense level of the counts in the Group,” the district court selected a base offense level of 16 for tax evasion under §§ 2T1.1 and 2T4.1.

Dale and Ashton argue that because the jury verdict did not identify the conspiratorial object, it was error for the district court to use the tax evasion base offense level without first determining that, were it-sitting as the trier of fact, it would convict the defendants of that offense. See U.S.S.G. § 1B1.2 application note 5; United States v. Tham, 948 F.2d 1107, 1115 (9th Cir.1991). The record, however, indicates that the district court did make the required determination of the object of the conspiracy and therefore the base offense level calculation was not erroneous. The district court, after considering the record, explained: “I find, first, that the base level that the court must consider in the case of Mr. Dale is a base level of 16, that is, conspiracy with an attempt to avoid taxes or tax evasion, rather than one based on false statements.” JA 1811. Further, as mentioned above, the court explicitly adopted the presentence reports and therefore adopted the conclusion of those reports that “[i]n this conspiracy, the defendants] [Dale and Ashton] attempted to evade both personal and corporate taxes.” JA 2775, 2814. See United States v. Terry, 916 F.2d 157, 160 (4th Cir.1990) (court may rely on presentence report for factual findings in setting defendant’s sentence); United States v. Murillo, 902 F.2d 1169, 1172 (5th Cir.1990) (same). Finally, since the jury convicted Dale and Ashton of the substantive offense of attempting to evade taxes, the district court could reasonably assume that the jury believed as well that tax evasion was an object of the conspiracy. See United States v. Hubbard, 889 F.2d 277, 279 (D.C.Cir.1989).

C. Tax Loss Computation

The defendants challenge the district court’s calculation of the corporate tax loss, first arguing that the $417,532 payment to the Swaffham and Gemona accounts and the $311,643 concealment of Korean corporate income should not have been included in the tax loss because these amounts were later properly accounted for in the 1986 tax returns. This argument is meritless because the calculation of tax loss for Guidelines purposes includes the amount the taxpayer “evaded or attempted to evade,” U.S.S.G. § 2T1.1, and therefore whether the conspirators completed the substantive offense is irrelevant for purposes of determining the offense level. See Hirschfeld, 964 F.2d at 324.

Next, the defendants contend that because the tax evasion object was not completed, the district court should have reduced their offense level by three levels under § 2X1.1(b)(2), which provides that

[i]f [the offense is] a conspiracy, decrease by 3 levels, unless the defendant or a co-conspirator completed all the acts the conspirators believed necessary on their part for the successful completion of the substantive offense or the circumstances demonstrate that the conspirators were about to complete all such acts but for apprehension or interruption by some similar event beyond their control.

The court’s decision not to grant the reduction was not clearly erroneous because the record indicates that the offense would have been completed but for Bowers’ resignation and refusal to turn over the incriminating tapes and documents he possessed. See United States v. Oyegbola, 961 F.2d 11, 13-14 (1st Cir.1992).

The defendants also argue that the district court should not have included certain amounts, alleged to be legitimate expenses, in calculating the corporate tax loss. The burden of proving mitigating sentencing factors was on the defendants, see United States v. Cuellar-Flores, 891 F.2d 92, 93 (5th Cir.1989), but they failed to identify and quantify the payments they alleged to be legitimate, with the exception of one $88,000 payment. Even assuming that the defendants carried their burden with respect to this $88,000, the total attempted tax loss would not have fallen below $1,000,000 and therefore the base offense level would not have changed.

Finally, Ashton and Dale argue that the district court erroneously treated certain amounts of the corporate tax loss as constructive dividends in calculating the personal tax loss. The parties agree that a defendant’s skimming of corporate receipts renders the defendant liable not only for the understatement of corporate income but also for the understatement of his personal income. See United States v. Knight, 898 F.2d 436, 437 (5th Cir.1990); United States v. Thetford, 676 F.2d 170, 175 (5th Cir.1982), cert. denied, 459 U.S. 1148, 103 S.Ct. 790, 74 L.Ed.2d 996 (1983). However, they argue that corporate funds diverted to the Swaffham and Gemona accounts and to Bourbonia should not have been treated as constructive dividends because they could not exercise control over the funds. In fact, however, the presentence reports, as adopted by the district court, characterized Swaffham and Gemona as “ ‘paper’ companies for they had no employees, just a bank account and mailing address in Hong Kong.” JA 2765. Further, the record indicates that Dale and Ashton controlled these companies as directors, as 75% shareholders and, until March 1987, as signatories to the corporate accounts. With regard to the transactions in Europe, the presentence reports explained that Dale and Ashton had accounts in Bourbonia and that funds diverted to that company were not for the purpose of paying legitimate business expenses. To evince Dale’s and Ashton’s control over these funds, the presentence reports noted that a portion of the ADM funds diverted to Bourbonia was subsequently transferred to ADM H & S, a company owned 75% by Dale and Ashton, for “their own benefit.” JA 2766. Accordingly, we do not think the district court erred in making the factual determination that the funds diverted from ADM to Swaffham, Gemona and Bourbonia should be considered constructive dividends because the funds came under the control of Dale and Ashton and the diversion was made primarily for their benefit. See Stone v. Commissioner, 865 F.2d 342, 343-44 (D.C.Cir.1989).

D. Upward Adjustment

The trial court adjusted upward the offense level for Dale by four levels and the offense level for Ashton by three levels for their respective roles in the criminal activities. Section 3B1.1 permits a four-level increase if “the defendant was the organizer or leader of a criminal activity that involved five or more participants or was otherwise extensive,” and a three-level increase if “the defendant was a manager or supervisor (but not an organizer or leader) and the criminal activity involved five or more participants or was otherwise extensive.” Dale and Ashton assert that their sentences must be remanded to the district court for an explicit finding on whether the upward adjustments were based on the extensiveness of the criminal activity or the fact that five or more persons participated. We disagree that a remand is necessary because the court’s adjustments could appropriately have been founded on either factor based on the facts adopted by the district court in the presen-tence reports for Dale and Ashton.

These reports, which the district court found to “set forth an adequate reflection of the facts,” JA 1811, specifically described the wide geographic reach of the criminal activity and the extensiveness of the actions taken to further the conspiracy, named Ashton and Dale as the leaders, and identified at least five persons who were involved in the scheme. Even more explicitly, the report for Dale stated he “was an organizer and leader in a criminal activity that involved more than five participants and was otherwise extensive.” JA 2815. The report for Ashton was similarly worded. JA 2776. Since the district court was entitled to rely on the presentence reports in determining the defendants’ sentences, see Murillo, 902 F.2d at 1172, we find no need for a remand.

E. Sweeney’s Downward Departure

In sentencing Sweeney, the district court departed downward from the applicable Guidelines range approximately two levels on the basis of a § 5K1.1 substantial assistance motion. On appeal, Sweeney complains that the extent of the departure, however, was based upon an improper application of the Guidelines because in sentencing him the district court impermissibly relied on a comparison to sentences typically imposed on drug couriers. We reject Sweeney’s claim. In Williams v. United States, a case where the defendant appealed the district court’s decision to depart upwards, the Supreme Court held that reviewing courts “must remand for sentencing: if the sentence was imposed as a result of an incorrect application of the Guidelines or if the sentence is an unreasonable departure from the applicable guideline range.” — U.S.-,-, 112 S.Ct. 1112, 1120, 117 L.Ed.2d 341 (1992). The appellant “bears the initial burden of showing that the district court relied upon an invalid factor at sentencing.” Id.

The government contends that appellate courts have no authority to review a defendant’s appeal of the extent of a downward departure, citing our pre-Williams decision in United States v. Hazel, 928 F.2d 420, 423-24 (D.C.Cir.1991). The Fourth Circuit, however, has decided otherwise:

If, as Williams held, a departure sentence may not stand unless a reviewing court determines that an invalid factor had no effect on the sentencing decision, it logically follows that an appellate court may not countenance a decision in which the district court extended an otherwise proper departure sentence based upon a circumstance that could not have supported a departure in the first instance. The reasoning of Williams dictates that a sentencing court may not consider in determining the extent of a departure from the guideline range a factor that would not constitute a valid basis for departure.

United States v. Hall, 977 F.2d 861, 865 (4th Cir.1992). For purposes of this case, we need not determine if Hazel and Hall are in conflict or determine the effect of Williams on Hazel. For even were we to review Sweeney’s sentence, we would conclude that remand is unnecessary because Sweeney did not meet his burden of showing that the district court relied on an invalid factor, i.e., a comparison to sentences imposed on drug couriers, in sentencing him.

The record indicates that the comparison was made not as a basis for the sentence but to provide a measure of comfort to Sweeney. The court began: “Now, these sentences you are possibly facing may seem harsh, but I think I should just draw a reference to other individuals who appear before this court day in and day out.” It explained with regard to drug couriers:

[T]hey face a mandatory sentence of ten years imprisonment, and the government takes a very hard view on whether or not they should be considered in certain circumstances as having given substantial assistance, so that they are taken out of that range. Ten years in prison, with no sophistication at all. So that’s one of the things that I also weigh in taking — in consideration of what should be done in any other cases.

JA 1885-86. Next, the district court clarified that it was “not in favor of the mandatory minimum in some cases, but that doesn’t apply here_” JA 1886. Viewing the statements as a whole, it appears that the district court was simply explaining to Sweeney that, by comparison, the sentences he faced were not that harsh. Moreover, the court made clear what factors it was relying on to make the approximate two-level departure, including: a comparison of the sentences imposed on Sweeney’s co-defendants; the fact that Sweeney had “already been given credit” for accepting responsibility; that “under the facts of the case” a departure to a probationary sentence was unwarranted; and that Sweeney had had “plenty of opportunity to stop” the scheme. JA 1886-89. Thus, while it might have been inappropriate for the district court to base Sweeney’s sentence even in part on the sentences imposed on drug couriers, see 18 U.S.C. § 3553(a)(6), we do not believe that Sweeney met his burden of showing that the district court actually relied on this factor.

F. Merger of Internal Revenue Code Offenses

All defendants contend that their convictions under 26 U.S.C. § 7206(1) (subscribing to a false tax return) and 26 U.S.C. § 7206(2) (aiding preparation of a false tax return) merge with their convictions under 26 U.S.C. § 7201 (tax evasion) because all the Internal Revenue Code counts rest on the same two deductions, both taken on the 1986 ADM tax return: the $500,000 accrued for software development and the $316,000 wire transfer to Bourbonia. In response, the government relies on the rule of statutory construction contained in Blockburger v. United States, 284 U.S. 299, 304, 52 S.Ct. 180, 182, 76 L.Ed. 306 (1932) (court should inquire “whether each provision requires proof of a fact which the other does not”). As a rule of statutory construction, however, Blockburger does not displace Congress’ own design. See Albernaz v. United States, 450 U.S. 333, 340, 101 S.Ct. 1137, 1143, 67 L.Ed.2d 275 (1981).

The Internal Revenue Code sets out a comprehensive scheme prohibiting and punishing tax fraud; section 7201, the “evasion” provision, has been called the “capstone” of this scheme. United States v. Helmsley, 941 F.2d 71, 99 (2d Cir.1991) (citing Spies v. United States, 317 U.S. 492, 497, 63 S.Ct. 364, 367, 87 L.Ed. 418 (1943)), cert. denied, — U.S. -, 112 S.Ct. 1162, 117 L.Ed.2d 409 (1992). As the pathmarking opinion explained, under appropriate circumstances, lesser section 7206 offenses merge with the “capstone” prohibition of section 7201:

[W]here proof of wilfully attempted evasion under § 7201 also proves, as an incident to the wilful evasion, the preparing and subscribing of a fraudulent return, the specific form of fraudulent conduct merges into the inclusive fraud charged under § 7201. To cumulate penalties beyond the maximum authorized by § 7201 is, therefore, improper under these circumstances.

United States v. White, 417 F.2d 89, 94 (2d Cir.1969) (emphasis added), cert. denied, 397 U.S. 912, 90 S.Ct. 910, 25 L.Ed.2d 92 (1970).

The interpretation of congressional intent advanced in White has been adhered to in sister circuits. See Helmsley, 941 F.2d at 99; United States v. Kaiser, 893 F.2d 1300, 1306 (11th Cir.1990); United States v. Pulawa, 532 F.2d 1301, 1302 (9th Cir.1976). United States v. Franks, 723 F.2d 1482, 1486-87 (10th Cir.1983), cert. denied, 469 U.S. 817, 105 S.Ct. 85, 83 L.Ed.2d 32 (1984), the case emphasized by the government, see Government Brief at 176, is not in conflict with White. In Franks, the charged section 7206 offense involved “[a] misrepresentation of foreign bank account information”; that offense was “distinct and independent from [the charged section 7201 offense,] an understatement of gross income.” Franks, 723 F.2d at 1487. The Franks court, far from disagreeing with the analysis presented in White, explicitly noted, with apparent approval, the government’s acceptance and distinction of that precedent. Id. at 1486; accord United States v. Sturman, 951 F.2d 1466, 1487-88 (6th Cir.1991), cert. denied, — U.S. -, 112 S.Ct. 2964, 119 L.Ed.2d 586 (1992); cf. Helmsley, 941 F.2d at 99-101 (counts involving criminal conduct beyond taxpayer’s evasion of personal income taxes do not merge).

The government, we note, did not cite, much less distinguish, the leading White decision. No cause has been shown for our departure from a precedent so far accepted by sister courts as guiding. We therefore hold that, on the facts here presented, the section 7206 “subscribing” and “aiding preparation of” false return convictions merge, as lesser included offenses, into the “capstone” section 7201 tax evasion convictions.

Given the absence of controlling D.C. Circuit precedent, the trial court correctly submitted the section 7206 and section 7201 counts to the jury. See, e.g., Garris v. United States, 491 A.2d 511, 514-15 (D.C.App.1985) (“Initially permitting convictions on both counts serves the useful purpose of allowing [the appellate] court to determine whether there is error concerning one of the counts that does not affect the other.”). We now remand, in view of our acceptance of the White analysis, and instruct the district court to vacate the sentences for the section 7206 offenses and to resentence the defendants pursuant to the section 7201 convictions. See Ball v. United States, 470 U.S. 856, 864-65, 105 S.Ct. 1668, 1673-74, 84 L.Ed.2d 740 (1985).

Conclusion

For the reasons stated, we affirm all the defendants’ convictions and remand with instructions to revise the sentences as required by Part X(F) of this opinion.

It is so ordered. 
      
      . Provisions in a "Status of Forces Agreement” prohibited ADM from doing business in Korea with any party other than the United States government.
     
      
      . Ownership of the other two corporations was transferred to Bowers and his wife for their own development.
     
      
      . On a visit to Korea, Dale gave Bowers a check from ADM for $50,000, purportedly to cover operating expenses. A deposit slip dated February 29, 1986, reflects a deposit to ADM’s Korean checking account of a $50,000 check, less $20,-000 received in cash. ADM’s check register characterizes the transaction as simply a $30,-000 deposit.
     
      
      . During a visit to Korea by both Dale and Ashton, Dale gave Bowers two checks, each in the amount of $50,000, for "Korea Operating Expenses” and instructed Bowers to give him two signed checks for $10,000 each, with the payee left blank. These checks were later dated June 3, 1986, and made out to the order of "D.C. National Bank" — the funds were apparently used by Ashton to purchase a condominium.
     
      
      . Bowers cashed a $10,000 check drawn on ADM’s Korean checking account and sent the proceeds to Ashton who was in Hong Kong.
     
      
      . At Dale’s request, Bowers wrote a $205,000 check on ADM's Korean account, payable to his wife; the check was deposited into the Bowers-es’ joint checking account and Bowers then wrote a personal check to Arlington for $200,-000.
     
      
      . At Dale’s direction, Bowers created three bogus invoices: two from Gemona, dated November 11 and December 15, 1986, seeking payment of, respectively, $89,000 and $185,422 for marketing and product studies, and one from Swaff-ham, dated December 15, 1986, seeking payment of $ 143,110 for consulting services. While visiting Washington, D.C. in December 1986, Bowers received from Segal three checks for the invoiced amounts, one signed by Ashton, the other two by Dale. Bowers deposited the checks into Gemona’s and Swaffham’s Hong Kong bank accounts.
     
      
      . In February 1987 Dale told Bowers to create invoices for the work from either Swaffham or Gemona. They decided on the $500,000 amount only after some'' discussion and apparently based on how much they thought they "cfould] get away with.” See infra note 36. Incident to the arrangement, Bowers created a phony "Software Development Contract,” backdated letters between Bowers and Swaffham and an invoice which he sent by 'facsimile to Dale.
     
      
      . Apparently, German law prohibited ADM itself from entering into or performing any contracts other than the Army contract that brought it to Germany.
     
      
      . As of that date the earlier partnership was dissolved and all of its business activities transferred to ADM H & S.
     
      
      . The new corporation was capitalized with $88,000 paid by ADM, allegedly in return for research performed by Knight. To support the payment, Sweeney prepared and signed what can only be a back-dated letter which “authorized Mr. Larry Knight acting in behalf of 'Hard- und Software Handelgeselleschaft mbH fuer Deutschland' [sic] (H & S), a company which is the process [sic] of being licensed to operate in West Germany, to begin a market project to provide the basic guidance required to form a business plan and direct the efforts of ADM into these new markets.” Joint Appendix 2032. The letter further stated: “Based on my negotiations, I estimate the cost of this project to be approximately $90,000. The project will be completed by the end of this year. I will develop a contract in the near future for your review and approval.” Id. The letter was dated January 12, 1986, some seven or eight months before ADM H & S’s corporate name was selected.
     
      
      . Ashton identified no other companies or offices for herself and for Dale identified only a nonprofit organization of which he was an officer.
     
      
      . At trial, Bowers explained:
      I believed that one of the problems, if I was to extricate myself from a situation that I had put myself in, was that I wanted it clear that it wasn't just me that was giving directions and replying to requests, and I just wanted the record clear in that respect, I wanted to make sure that I was protected.
      JA 1097.
     
      
      . Bowers testified at trial: "I didn’t want the money to be moved and then me made out to be — you know, everything tried to be erased like it never happened, and I be put in a position where I could be accused of things.” JA 1109.
     
      
      . At one point, Bowers was presented with a proposed settlement agreement under which he was to indemnify ADM, Ashton and Dale for any liability arising from the Korean activities, to refrain from testifying against them in a pending lawsuit by another ADM vice president, Chuck Roth, to acknowledge certain facts regarding Roth's terms of employment, to give up all interest in ADM Asia, Gemona and Swaff-ham and to "turnover [sic] to M. Ashton all documents, tapes, statements and evidence of any kind which he or Roth may ever have intended to use against [ADM, Ashton and Dale].” JA 2715.
     
      
      . There is no apparent explanation in the record for the discrepancy between the amounts Ashton and Dale reported to the IRS, $40,000 and $10,000 respectively, and the amounts each received according to Bowers' testimony, $30,-000 and $20,000 respectively. See supra pp. 825-26.
     
      
      . August 21, 1987 is the date that appears on the note’s face but it is unlikely that both Dale and Ashton signed it on that day since it appears Ashton was then in Korea and Dale was in Washington.
     
      
      .A document from Dale’s and Ashton’s personal accountant’s file indicates that as of February 29, 1988, the “Guam National Bank loan” was still outstanding and no payments had been made, although the next entry states: "Paid w/ $206,250 capital contribution from David M. Dale, $200,000 loan, $6250 interest." Trial Transcript 3073-75. The accountant testified that he had no personal knowledge of the repayment but had merely been informed of it by Dale.
     
      
      . Count 1 specifically identified as acts of the tax evasion conspiracy the following transactions: the deduction of the $417j532 Gemona payment, the $500,000 Swaffham accrual and the $316,000 and $102,655 Bourbonia payments, the failure to treat as income the $200,000 Arlington disbursement and the $50,000 payments to Dale and Ashton and the creation of phony explanations in amended returns for the initial treatment of the $500,000 accrual, the $316,000 payment and the $50,000 payments.
     
      
      . For the same reasons, we also reject ADM’s sufficiency challenge which adopts Ashton's arguments by reference. See ADM Brief at 8.
     
      
      . This section provides:
      Whoever, in any matter within the jurisdiction of any department or agency of the United States knowingly and willfully falsifies, conceals or covers up by any trick, scheme, or device a material fact, or makes any false, fictitious or fraudulent statements or representations, or makes or uses any false writing or document knowing the same to contain any false, fictitious or fraudulent statement or entry, shall be fined not more than $10,000 or imprisoned not more than five years, or both.
      18 U.S.C. § 1001.
     
      
      . See, e.g., United States v. Gahagan, 881 F.2d 1380 (6th Cir.1989); United States v. Race, 632 F.2d 1114, 1120 (4th Cir.1980); United States v. Vesaas, 586 F.2d 101, 104 (8th Cir.1978); United States v. Anderson, 579 F.2d 455, 459-60 (8th Cir.), cert. denied, 439 U.S. 980, 99 S.Ct. 567, 58 L.Ed.2d 651 (1978); United States v. Diogo, 320 F.2d 898, 906-07 (2d Cir.1963).
     
      
      . Ashton asserts the record does not establish she was a legal owner or director of the two Hong Kong corporations before she signed the cited DOD forms because (1) corporate minutes indicate the transfer of ownership in the company was approved only "subject to stamping,” meaning subject to stamping by the Stamp Duty Office in Hong Kong, and there is no evidence stamping occurred before the forms were completed in late January and early February 1987; (2) notices of change of directors for the two Hong Kong corporations were not filed with the Hong Kong Registrar of Companies until February 27, 1987; and (3) a- letter dated March 12, 1987, from Edwards to a Hong Kong law firm noted that the firm "had never received new bank signature cards nor any documents effecting change of directors and transfer of shares” and stated: "If you could effect such changes and provide the bank with the appropriate signature cards I would be most appreciative.” JA 2744.
     
      
      . See Webster’s Third New International Dictionary 481 (1981) (defining "connection" as "the state of being connected or linked” and as "a social, professional, or commercial relationship in a practical or active way”).
     
      
      . The Gemona and Swaffham corporate minutes of meetings conducted October 21, 1986 note that Dale, Ashton and Bowers were "appointed as Directors ... with immediate effect." JA 2106, 2127. In addition, Ashton signed a notice that she "consented to act as Director” of each corporation "as from October 21, 1986,” JA 2109, 2129, and in fact attended a shareholder’s meeting for each on November 2, 1986, the minutes of which reflect that a "shareholder vote” “did unanimously resolve” to increase the outstanding shares in each corporation to 100: 37.5 for Dale, 37.5 for Ashton and 25 for Bowers. JA 2131, 2110.
     
      
      . Our disposition here applies equally to Dale’s adoption by reference of the same argument to challenge his conviction on count 9. See Dale Brief at 1.
     
      
      . In light of this disposition, we need not decide whether, as other circuits have held, it is a misrepresentation’s potential to influence, irrespective of the recipient’s knowledge vel non of its falsity, that determines materiality under section 1001. See United States v. Whitaker, 848 F.2d 914, 916 (8th Cir.1988); United States v. Goldfine, 538 F.2d 815, 8820-21 (9th Cir.1976). We note in this regard, however, that this Circuit has consistently held:
      The test of materiality is whether the statement “has a natural tendency to influence, or was capable of influencing, the decision of the tribunal in making a [particular] determination." Proof of actual reliance on the statement is not required; the Government need only make a reasonable showing of its potential effects.
      
        Hansen, 112 F.2d at 949 (quoting United States v. Diggs, 613 F.2d 988, 999 (D.C.Cir.1979), cert. denied, 446 U.S. 982, 100 S.Ct. 2961, 64 L.Ed.2d 838 (1980)), cert. denied, 475 U.S. 1045, 106 S.Ct. 1262, 89 L.Ed.2d 571 (1986); see also Weinstock v. United States, 231 F.2d 699, 701-02 (D.C.Cir.1956).
     
      
      . This subsection provides in part: Any person who-
      Willfully aids or assists in, or procures, counsels, or advises the preparation or presentation under, or in connection with any matter arising under, the internal revenue laws, of a return, affidavit, claim, or other document, which is fraudulent or is false as to any material matter, whether or not such falsity or fraud is with the knowledge or consent of the person authorized or required to present such return, affidavit, claim, or document; ...
      shall be guilty of a felony and, upon conviction thereof, shall be fined not more than $100,000 ($500,000 in the case of a corporation), or imprisoned not more than 3 years, or both, together with the costs of prosecution.
      26 U.S.C. § 7206(2).
     
      
      . This section provides:
      Any person who willfully attempts in any manner to evade or defeat any tax imposed by this title or the payment thereof shall, in addition to other penalties provided by law, be ■ guilty of a felony and, upon conviction thereof, shall be fined not more than $100,000 ($500,000 in the case of a corporation), or imprisoned not more than 5 years, or both, together with the costs of prosecution.
      26 U.S.C. § 7201.
     
      
      . This statute provides:
      Whoever, having devised or intending to devise any scheme or artifice to defraud, or for obtaining money or property by means of false or fraudulent pretenses, representations, or promises, transmits or causes to be transmitted by means of wire, radio, or television communication in interstate or foreign commerce, any writings, signs, signals, pictures, or sounds for the purpose of executing such scheme or artifice, shall be fined not more than $1,000 or imprisoned not more than five years, or both. •
      18 U.S.C. § 1343.
     
      
      .The court noted that "[i]n determining whether the government has met its burden of proof, ... no legal distinction may be drawn between direct and circumstantial evidence.” 760 F.2d at 333 (citing United States v. Davis, 562 F.2d 681, 684 (D.C.Cir.1977)).
     
      
      . She signed the August 25, 1988, amended 1986 return which gave a phony explanation of why the $316,000 payment had been deducted.
     
      
      . This conclusion also disposes of Dale’s adoption by reference of the same challenge to his convictions. See Dale Brief at 1.
     
      
      . The government also urges strongly that the alleged consultation work performed in 1986 is inconsistent with Knight’s testimony that to the best of his knowledge Sweeney first met Worm-er on December 10, 1986, when Sweeney and Knight drove together to Wormer’s home. What Knight actually said, however, is that as far as he knew that was the first occasion Sweeney and Wormer "physically met," suggesting they had had previous contact by telephone or otherwise. See JA 1130.
     
      
      . According to a Grant Thornton accountant, when asked why the related party transactions had not been disclosed, Segal responded "No one asked me." JA 1542.
     
      
      . Segal wrote Bowers a letter dated March 5, 1987, stating that “a bill is needed for the consulting work that David Dale requested. My understanding is that the work was performed last year for a total cost of approximately $150,-000. The consultant’s report is also needed as backup to the bill.” JA 2055. When Bowers subsequently received an invoice for $149,000 in mid-March, he made a call to Dale which he recorded. During that conversation Bowers reminded Dale of a previous agreement regarding the invoice amount: “We agreed for 750, and then we were to back ... back it down to 500. Remember, I was to prepare some paper work, two or three exchanges, and, uh, it was to be backed down to 500.” JA 2387. Later in the conversation, Dale remarked “I don’t know whether Marty can handle seven hundred and fifty thousand," JA 2389, and that they would “have to find out what Marty thinks we can get away with,” JA 2391. The actual $500,000 invoice arrived at ADM a week later, back-dated to December 30, 1986. Segal informed Grant Thornton of the amount sometime before March 15, 1987.
     
      
      .During the negotiations, Ashton and Bowers attempted to persuade Bowers to sign a document agreeing to hand over the incriminating recordings and acknowledging that the $200,000 payment to Arlington had been “formally loaned” by ADM Asia. See JA 2714-15. In addition, handwritten notes made by Segal while in Korea reveal his knowledge of the tapes and Ashton’s desire to obtain them and expressly indicate that “money was laundered" through the Korean office. JA 2058.
     
      
      . He said nothing at that time about the $200,-000 Arlington payment or the $500,000 Swaff-ham accrual.
     
      
      . The accountant testified that "the substance” of Segal's explanation was that "some bills had been paid by ADM U.S. ... and that the expenses were really incurred by a related corporation, ADM GmbH,” referring to ADM H & S. Tr. 3176. In fact, the invoices were unrelated to ADM H & S.
     
      
      . At a hearing conducted February 22, 1991, Sweeney, pursuant to an agreement with the government, provided extensive sentencing testimony regarding ADM's business activities, some of which suggested Segal may not have been directly involved in ADM’s fraudulent conduct.
     
      
      . Segal maintains that comments made by the trial judge at sentencing indicate he applied the wrong standard, deferring entirely to the jury's judgment and abdicating his responsibility to review the evidence himself. The challenged language states:
      [I]n looking at the verdict of the jury, the court cannot sit back and say to the jury, "I disagree." Whether I disagreed with their verdict in your case, and I’m not going to tell you whether I did or did not, but whether I disagreed with the jury verdict in your case is of no moment. That isn’t a basis for setting aside the verdict or giving you a new trial. There are standards that the court must follow, and with respect to the evidence, as long as the evidence has been presented to the jury in a fair manner and under fair and correct instructions, and as long as the court has decided and concluded that the jury has considered those matters, it’s a verdict for the jury to decide, it’s not for the court.
      JA 1825-26 (emphasis added). The highlighted language satisfies us that the judge properly assessed the jury’s verdict in light of the credible evidence and the weight one could reasonably ascribe to it.
     
      
      . In Chirino, this court stated:
      To assess the reasonableness of [the NTSB’s] interpretation, we pause to observe that, in an admittedly different but analogous context, cases construing Rule 33 of the Federal Rules of Criminal Procedure governing new trials are instructive on the question of what constitutes "newly discovered" evidence. In the Rule 33 setting, several courts have concluded that post-trial testimony of a co-defendant who initially asserted his or her Fifth Amendment privilege does not constitute "newly discovered” evidence within the meaning of the Rule....
      These decisions from the criminal law setting provide a direct analogy to the situation before the Board in this case.
      849 F.2d at 1532 (citations to Metz, Diggs and Jacobs omitted).
     
      
      . In Vest, the court rejected the defendant’s position that suppression is appropriate under Title III if any part of the motivation is criminal or tortious, explaining:
      It is characteristic of human experience that individuals usually — perhaps even always— act with mixed motives. To adopt the interpretation of the statute advanced by the defendant would impose on the government the nearly insurmountable burden of eliminating the possibility that an improper motive played any part in the decision to intercept the communication.
      639 F.Supp. at 904.
     
      
      . The circuits are split on the question whether a district court's decision not to hold a Franks hearing is reviewed under the clearly erroneous or de novo standard of review. Four circuits adhere to the clearly erroneous standard. See United States v. Buchanan, 985 F.2d 1372, 1378 (8th Cir.1993); United States v. Skinner, 972 F.2d 171, 177 (7th Cir.1992); United States v. Hadfield, 918 F.2d 987, 992 (1st Cir.1990), cert. denied, — U.S. -, 111 S.Ct. 2062, 114 L.Ed.2d 466 (1991); United States v. One Parcel of Property, 897 F.2d 97, 100 (2d Cir.1990). Two review such decisions de novo. See United States v. Homick, 964 F.2d 899, 904 (9th Cir.1992); United States v. Mueller, 902 F.2d 336, 341 (5th Cir.1990). We have not definitively resolved the issue in this circuit. In United States v. Richardson, 861 F.2d 291, 293 (D.C.Cir. 1988), cert. denied, 489 U.S. 1058, 109 S.Ct. 1325, 103 L.Ed.2d 593 (1989), we invoked the clearly erroneous standard to review a district court’s finding on the good faith belief of the police officer in executing the disputed affidavit but we did not explicitly discuss which standard would apply to the ultimate decision not to hold a Franks hearing. For purposes of this case, we need not resolve the precise scope of Richardson or take sides in the circuit conflict because we find that the district court’s decision not to hold a hearing passes muster under either standard of review.
     
      
      . The government asserts that arguments relat- . ing to the affiant’s alleged misrepresentation of Bowers’ credibility .have been waived because they were not raised below. See Government Brief at 44 n. 18. However, in their Memorandum in Support of Motion to Suppress Tangible Evidence and Its Fruits Seized in Search of ADM Offices, the defense counsel complained of the "bias of Bowers” who "himself was under investigation.” JA 240-41. Further, at the argument on the suppression motion, defense counsel reiterated this concern.
     
      
      .The defendants also argue that the affiant’s failure to disclose that Bowers had previously given several contradictory statements to two different government agents also warranted a Franks hearing. However, the district court carefully considered the alleged discrepancies and found that, by and large, each could be "effortlessly harmonized.” Warehouse Memorandum at 10-12. Further, as indicated above, the district court reasoned that "[e]ven if [the magistrate] had rejected Bowers' statements as coming from a source unworthy of belief, she would still be left with the sufficient content in the warrant affidavit to support a finding of probable cause ‘because the tainted information ... was merely cumulative of criminal activity.’ ” Id. at 13 (quoting United States v. Grunsfeld, 558 F.2d 1231, 1240 (6th Cir.), cert. denied, 434 U.S. 872, 98 S.Ct. 219, 54 L.Ed.2d 152 (1977)). We have no cause to disturb these conclusions.
     
      
      . The defendants also allege that the agent misrepresented in her affidavit that informant Charles Roth had knowledge of ADM’s tax evasion because Corboy reported that Roth told him that he had no independent knowledge of ADM’s tax evasion. However, Agent Shintani’s affidavit did not purport to reflect Roth’s independent knowledge but stated only that Roth knew of the establishment of dummy corporations for the purpose of evading taxes.
     
      
      . In their supplemental brief, the defendants assert that the district court may have erroneously subjected them to the higher burden of actually establishing the affiant’s reckless disregard for the truth because at one point the court stated that the defendants had not "shown that the affiant in fact entertained serious doubts as to the truth of [her affidavit].” Warehouse Memorandum at 17 (internal quotation omitted) (emphasis added). However, it is abundantly clear to us that the district court, which repeatedly correctly noted that the defendants were required to make only a substantial preliminary showing of the affiant’s reckless disregard for the truth, see Warehouse Memorandum at 5, 7, 8, 21, recognized and applied the correct legal standard and in the single passage cited by the defendants was merely substituting the abbreviated “shown" for the more cumbersome “made a substantial preliminary showing."
     
      
      . In Maxwell, a statement in the warrant that the magistrate had found the supporting affidavit to establish probable cause did not constitute a sufficient incorporation. 920 F.2d at 1032; see also United States v. George, 975 F.2d 72, 76 (2d Cir.1992) (warrant which stated that "it is ‘issued upon the basis of an application and affidavit[ ] of Patrolman Brickell does not direct the executing officers to refer to the affidavit for guidance concerning the scope of the search and hence does not amount to incorporation by reference”). However, the Maxwell court continued:
      Although we hold that the warrant in this case did not incorporate the affidavit by reference, we recognize that the "realities of administration of criminal justice," Moore v. United States, 461 F.2d at 1238, counsel against an overly exacting standard for determining when a warrant successfully incorporates a supporting affidavit. In this case, we believe it would have been sufficient if the warrant, in addition to referencing “Attachment # 2” [a list of items to be seized] in the space provided for describing the items to be seized, had also made some reference in that space to the affidavit or to "Attachment # 3,” which is how the affidavit was captioned in the warrant application presented Jo the magistrate.
      920 F.2d at 1033 n. 4. In the present case, the references in the warrant to the affidavit were not made with regard to probable cause nor were they simply descriptive of the background of the warrant. Instead, the warrant expressly incorporated the Shintani affidavit and thereby limited the permissible scope of the government’s search.
     
      
      . “Separate conspiracy” is the defendants' characterization. The scope of the conspiracy here, however, was a question of fact within the jury’s ken; a single conspiracy indeed may include both tax evasion and its concealment. See, e.g., United States v. Cunningham, 723 F.2d 217, 228-29 (2d Cir.1983), cert. denied, 466 U.S. 951, 104 S.Ct. 2154, 80 L.Ed.2d 540 (1984).
     
      
      . Defendants emphasize the instruction that the jury could convict if it found "that the Government has established beyond a reasonable doubt that any one of these items was falsely reported on the return.” Tr. 4533.
     
      
      . Defendants also argue that this omission, and other errors asserted in connection with the section 1001 convictions, affect the conspiracy convictions. Because we uphold the section 1001 convictions, we do not reach this argued interrelationship.
     
      
      . See Criminal Jury Instructions for the District of Columbia, No. 2.09 at 46 (3d ed. 1978) (substantially identical language). In Moore v. United States, 345 F.2d 97, 98 & n. 1 (D.C.Cir.1965), we approved a similarly worded charge.
     
      
      . The district court held: "I find for the purpose of the record that the presentence reports in this record set forth an adequate reflection of the facts presented in this case.” JA 1811.
      Pursuant to 18 U.S.C. § 3742(d)(2), the pre-sentence reports were made a part of the record on appeal, and under this circuit's protocol, were filed with this court under seal. In considering the defendants’ objections to their sentencing, we have, of course, had occasion to review these reports in their entirety. For purposes of this opinion, however, we cite only to specific statements in those reports which defendants have explicitly discussed and objected to in their publicly filed briefs on appeal, their publicly filed submissions to the district court under Fed.R.Crim.P. 32(c)(3) or their statements in open court at sentencing under Fed.R.Crim.P. 32(a)(1)(B).
     
      
      . Section 3D 1.2 provides in part that “[a] II counts involving substantially the same harm shall be grouped together into a single Group.” The presentence reports stated: "Since these object offenses involved acts that were part of the same course of conduct or common scheme or plan and substantially the same harm, they are grouped according to section 3D1.2." JA 2774.
     
      
      . Ashton argues additionally that these amounts should not be attributed to her because the evidence did not establish that she had joined the conspiracy at the time of these transactions. However, according to the facts in the presentence reports, as adopted by the district court, see supra note 54, Ashton was a member of the conspiracy in 1986 when these events transpired.
     
      
      . At sentencing, the district court briefly addressed this contention, stating that “[w]ith respect to the argument as to an incomplete conspiracy and a request that the court depart downward for that, I conclude that that argument must be rejected.” Sentencing Transcript at 80. The presentence reports, which the district court adopted, see supra note 54, made even clearer that an offense level adjustment was unwarranted because the defendants’ "attempts to cover up the criminality that underlay their conduct” was “precipitated by actions of co-conspirator David Bowers.” JA 2770.
     
      
      . At sentencing, the district court stated that "[w]ith respect to Mr. Dale’s role in the offense ... it seems to me that under the facts of this case ... as the jury has found them and as the court has heard the evidence, Mr. Dale must be assigned a plus four.” Regarding Ashton’s role, the court explained: “I do see a distinction here, ... I find that Ms. Ashton should be assigned ... a three, rather than a four.”
     
      
      . Section 5K1.1 provides: "Upon motion of the government stating that the defendant has provided substantial assistance in the investigation or prosecution of another person who has committed an offense, the court may depart from the guidelines.”
     
      
      . Cf. Sansone v. United States, 380 U.S. 343, 349, 85 S.Ct. 1004, 1009, 13 L.Ed.2d 882 (1965) (26 U.S.C. §§ 7203, 7207 are lesser included offenses within § 7201 in appropriate cases); 
        United States v. McGill, 964 F.2d 222, 239-40 (3d Cir.) (same), cert. denied, — U.S.-, 113 S.Ct. 664, 121 L.Ed.2d 588 (1992); United States v. Doyle, 956 F.2d 73, 75 (5th Cir.1992) (same).
     
      
      . The lesser included offense analysis of White does not spill over to embrace prosecutions for Internal Revenue Code offenses plus offenses under other statutes with discrete objectives. Cf. supra Part V (on coupling tax code and wire fraud convictions); United States v. Woodward, 469 U.S. 105, 106-10, 105 S.Ct. 611, 612-13, 83 L.Ed.2d 518 (1985) (sustaining convictions, based on same act, under 18 U.S.C. § 1001 for making false statement to agency of United States and under 31 U.S.C. §§ 1058, 1101 for willfully failing to report defendant was carrying over $5000 into the United States).
     