
    UNITED STATES of America, Plaintiff-Appellee, v. Samuel J.T. MOORE, III, Defendant-Appellant.
    No. 11-4684.
    United States Court of Appeals, Fourth Circuit.
    Argued: Sept. 19, 2012.
    Decided: Nov. 28, 2012.
    
      ARGUED: David G. Barger, Greenberg Traurig, LLP, McLean, Virginia, for Appellant. Joseph Brian Syverson, United States Department of Justice, Washington, D.C., for Appellee. ON BRIEF: Lee W. Kilduff, Law Office of Lee W. Kilduff, Richmond, Virginia, for Appellant. Kathryn Keneally, Assistant Attorney General, Frank P. Cihlar, Chief, Criminal Appeals & Tax Enforcement Policy Section, Gregory Victor Davis, United States Department of Justice, Washington, D.C.; Neil H. MacBride, United States Attorney, Alexandria, Virginia, for Appellee.
    Before DUNCAN and DAVIS, Circuit Judges, and TIMOTHY M. CAIN, United States District Judge for the District of South Carolina, sitting by designation.
   Affirmed by unpublished opinion. Judge DAVIS wrote the opinion, in which Judge DUNCAN and Judge CAIN joined.

Unpublished opinions are not binding precedent in this circuit.

DAVIS, Circuit Judge:

Appellant Samuel J.T. Moore, III (“Moore”), owned and operated Club Velvet (“the Club”), a strip club in downtown Richmond, Virginia. A jury convicted him of tax offenses relating to tax years 2005, 2006, and 2007. He appeals his convictions on various grounds, including sufficiency of the evidence, as well as the district court’s denial of his motion to suppress evidence seized during a search of the Club. He also challenges his sentence. For the following reasons, we affirm.

I.

A.

In 2000, Moore opened Club Velvet as a sole proprietorship (i.e., a Schedule C corporation), and registered the business as L.A. Diner. The Club (and thereby Moore) received income from various sources. For purposes of this case, the Club’s income fell into six main categories:

The first income category comprised cover charges, which were tracked by “do-orwatehers.”

The second income category comprised dancer fees and fines. These were payments by dancers of the Club’s share of payments (by patrons to the dancers) for lap dances (ranging from $20 to $30), and fines for “violations” of Club rules, such as failing to perform a minimum number of dances. The amount the dancers owed in fees and fines was tracked by a “dance-watcher.” Several dancewatcher notebooks, which tallied dances and fines, were recovered during the search of the Club.

The third income category comprised disc jockey payments. Under the procedures implemented by Moore, each of the dancers paid the DJ $40 per night, and the DJ turned over half of those payments to the Club.

The fourth income category comprised fees, ranging from $10 to $20, the Club received on cash advances to customers on their credit cards.

The fifth income category comprised fees the Club received beginning on August 5, 2005, when three ATMs installed the previous month became operational. These were fees paid by patrons withdrawing cash from the ATMs.

The sixth and final category comprised income from the sale of food, drinks (including $250 bottles of champagne, which gave patrons access to the Club’s third-floor “champagne room”), and tobacco products, as well as from pool table rentals.

Moore relied on his accountant, Greg Jonson (“Jonson”), to prepare his individual tax returns, which included the Club’s income on Schedule C. To the extent Moore reported the Club’s income to Jonson he did so using hand-written forms called “daily sheets,” which listed the Club’s revenue in each of several categories: food, drinks, and cigars; cover charges; lap dances; pool table rentals; and fines. Moore also used the daily sheets to report to Jonson the amounts he deposited in the Club’s bank account. Some deposits were from the minority of patrons who used credit cards, and were deposited directly into the L.A. Diner account. Most patrons, however, paid with cash. On the daily sheets, Moore reported the amount deposited as “cash to bank.” But the credit card revenue and “cash to bank” totals did not account for the full amount of the Club’s revenue, because Moore was using another avenue to, in effect, deposit cash in the bank; that is, on a nightly basis, Moore replenished the cash held in the three ATMs he had installed in July 2005. Each time a patron withdrew cash from an ATM, the funds were debited from the patron’s bank account and credited, along with a fee, to the L.A. Diner account. The sums Moore deposited in the Club’s account in this manner equaled $256,660 in 2005, $776,260 in 2006, and $693,980 in 2007.

To summarize, there were three ways the Club’s revenue was deposited in the L.A. Diner bank account: (1) credit card payment transfers; (2) cash deposited directly into the bank; and (3) cash used to replenish the ATMs, which was indirectly deposited in the bank when a customer withdrew the cash from the ATM.

B.

In August 2007, the Virginia Department of Alcoholic Beverage Control (“ABC”) began investigating the Club after receiving complaints that it was serving alcoholic beverages to underage customers, serving alcohol after hours, and allowing fully nude lap dances, any one of which would have constituted violations of Virginia law. Undercover ABC agents visited the Club several times in late 2007 and observed the violations that were the subject of the complaints. Meanwhile, the Richmond Police Department (“RPD”) had also begun investigating the Club, although for different alleged offenses. Detective Sergeant Steve Ownby (“Ownby”) had learned from a confidential informant, a former dancer at the Club who was Moore’s ex-girlfriend, that Moore was engaged in illegal narcotics and prostitution activities. See United States v. Moore, 775 F.Supp.2d 882, 886 (E.D.Va.2011) (“Moore I”).

Ownby’s investigation led him to seek the assistance of Robin Rager (“Rager”), a Special Agent at the federal Internal Revenue Service. Ownby and Rager had worked together previously during other investigations. Id. Ownby contacted Rag-er on August 31, 2007, because he knew that Rager “had expertise that would be helpful in analyzing financial aspects of the investigation.” Id.

Sometime in September or October 2007, Ownby contacted a state prosecutor, Shannon Taylor, about the possibility of convening a grand jury investigation into the suspected illegal activities at the Club. Around the same time, the ABC agents also separately contacted Taylor about the evidence they had gathered. The ABC and RPD then continued a joint investigation and conducted additional undercover visits to the Club. Around this same time, in November 2007, Rager opened an IRS “Primary Investigation.” Id. In connection with Moore’s later motion to suppress, the district court found that the purpose of opening the investigation was to “provide assistance and resources to Sgt. Ownby’s state investigation” and to “account for her time for administrative purposes.” Id.

In February 2008, Ownby began to prepare an application for a search warrant. The execution date for the warrant was accelerated after the RPD received a report from a woman who alleged that Moore was having an “inappropriate sexual relationship” with her underage daughter. Id. at 887. A state judge issued the warrant on February 22, 2008, and it was executed early the next day. The warrant authorized the police to search for evidence of prostitution (Va.Code §§ 18.2-346, 18.2-347, 18.2-348, 18.2-357), bestiality (Va.Code § 18.2-361), public nudity (Richmond City Code § 66-249), and drug distribution (Va.Code § 18.2-248). The police officers who conducted the search were accompanied by ten IRS agents and four agents from the federal Bureau of Alcohol, Tobacco, and Firearms (ATF). Ownby sought the assistance of the federal agents for two reasons: (1) “it was expected that the search would yield a substantial volume of documentary evidence to be catalogued,” and “the RPD lacked sufficient staff to conduct the document-intensive search and to manage the search in an orderly fashion”; and (2) “Sgt. Ownby decided that it was necessary to keep search preparation completely secret, even from other RPD sections.” Moore I, 775 F.Supp.2d at 887. The state officers, assisted by the federal agents, executed the search warrant and seized documents and money from the Club.

Ultimately, Moore was not charged with the state offenses underlying the search warrant. Instead, on September 7, 2010, he was indicted by a federal grand jury in the Eastern District of Virginia on two charges of tax fraud. On October 6, 2010, the grand jury returned a three-count superseding indictment. Counts One and Two charged Moore with making and subscribing a false tax return for tax years 2005 and 2006, respectively, in violation of 26 U.S.C. § 7206O). Count Three charged Moore with tax evasion for tax year 2007, in violation of 26 U.S.C- § 7201.

Moore was tried from February 7 through 15, 2011, and convicted on all three counts. The district court sentenced him to 78 months’ imprisonment followed by three years of supervised release, and imposed a $250,000 fine. Moore filed a motion for a new trial and a motion for a judgment of acquittal on Count One. The district court denied each in separate memorandum opinions. Moore timely appealed.

II.

Moore first argues that the evidence produced at trial was insufficient to support his conviction on Count One, relating to tax year 2005. This alleged insufficiency also, in Moore’s view, entitles him to a new trial on Counts Two and Three.

We begin by explaining a bit more about the charges Moore faced. Count One charged Moore with making and subscribing a false tax return, in violation of 26 U.S.C. § 7206(1), for tax year 2005. Moore’s tax return for 2005 reported gross business receipts of $546,887. The government argues that the trial evidence showed that Moore willfully understated the Club’s gross receipts for 2005 by $34,400. Count Two also charged fraudulent underreport-ing of income, for tax year 2006. For that year Moore reported gross Club receipts of $688,304, which the government argues understated his actual income by $354,050.

Count Three was somewhat different, because Moore did not file a tax return for tax year 2007. He did, however, report some of the Club’s income to his accountant, although the government sought to prove that the reported amount understated his actual income for 2007, just as the reported income was understated for 2005 and 2006. The amount Moore reported to his accountant as the Club’s gross receipts was $808,470. The government argues the evidence shows that this number understated the Club’s 2007 receipts by $255,506. The statute under which Moore was charged for tax year 2007 was not § 7206(1), because he did not actually file a return, but rather 26 U.S.C. § 7201.

“We review the sufficiency of the evidence to support a conviction by determining whether there is substantial evidence in the record, when viewed in the light most favorable to the government, to support the conviction.” United States v. Palacios, 677 F.3d 234, 248 (4th Cir.2012) (quotation marks omitted). “[I]n the context of a criminal action, substantial evidence is evidence that a reasonable finder of fact could accept as adequate and sufficient to support a conclusion of a defendant’s guilt beyond a reasonable doubt.” United States v. Burgos, 94 F.3d 849, 862 (4th Cir.1996) (en banc).

To prove a violation of 26 U.S.C. § 7206(1), the government must prove that “(1) the defendant made and subscribed to a tax return containing a written declaration; (2) the tax return was made under penalties of perjury; (3) the defendant did not believe the return to be true and correct as to every material matter; and (4) the defendant acted willfully.” United States v. Aramony, 88 F.3d 1369, 1382 (4th Cir.1996). As to Count Three, in order to obtain a conviction for income tax evasion under 26 U.S.C. § 7201, the government must prove “[1] willfulness, [2] a substantial tax deficiency, and [3] an affirmative act constituting an attempted evasion of the tax.” United States v. Goodyear, 649 F.2d 226, 227-28 (4th Cir.1981). “In order to prove a tax deficiency, the government must show first that the taxpayer had unreported income, and second, that the income was taxable.” United States v. Abodeely, 801 F.2d 1020, 1023 (8th Cir.1986) (internal quotation marks omitted).

One way to prove a defendant’s actual income is through direct evidence. As the Eighth Circuit has explained, however, such evidence is rare:

Proof of unreported taxable income by direct means is extremely difficult and often impossible. By the very fact that a taxpayer has failed to report the income, it behooves him to obscure any trace of its existence. Therefore, direct methods of proof, which depend on the taxpayer’s voluntary retention of records of the income, fail. Accordingly, the government has armed itself with an arsenal of indirect methods of proof which rely on circumstantial evidence to disclose unreported taxable income.

Id. Nonetheless, the government here did present direct evidence, which it called “specific-items evidence.” The specific-items evidence mainly consisted of documents seized from the Club that, the government argued, showed the Club received significantly more income than was reported on Moore’s tax returns.

The government did not rely solely on the specific-items evidence, however. Rather, as in many § 7206(1) cases, the government also sought to prove that the Club’s receipts were higher than those reported through a circumstantial method of proof: here, a modified version of the “bank-deposits” method.

Under [the bank-deposits] method, all deposits to the taxpayer’s bank and similar accounts in a single year are added together to determine the gross deposits. An effort is made to identify amounts deposited that are non-taxable, such as gifts, transfers of money between accounts, repayment of loans and cash that the taxpayer had in his possession prior to that year that was deposited in a bank during that year. This process is called “purification.” It results in a figure called net taxable bank deposits.
The government agent then adds the amount of expenditures made in cash.... The total of this amount and net taxable bank deposits is deemed to equal gross income. This is in turn reduced by the applicable deductions and exemptions. The figure arrived at is considered to be “corrected taxable income.” It is then compared with the taxable income reported by the taxpayer on his return.

United States v. Boulet, 577 F.2d 1165, 1167 (5th Cir.1978) (footnote omitted) (quoted in United States Department of Justice Criminal Tax Manual, § 33.01 (2008)).

The government presented its specific-items evidence and its bank-deposits evidence as independent, alternative methods of proof. As the district court instructed the jury:

Both of [these] methods are acceptable methods of proving unreported income. They should be viewed by you independently, and you can use either one of them, or you can use both of them for any and all tax years in deciding whether the government has proved the elements of the crimes charged beyond a reasonable doubt.

J.A. 1320.

As we describe below, each of the government’s methods of proof is independently sufficient to support the verdict here.

A.

We first examine the sufficiency of the government’s specific-items evidence. The specific-items evidence did not account for all of Moore’s alleged unreported income, but it did not need to; to convict Moore, the jury needed to find only that Moore willfully understated the Club’s gross receipts by some “material” amount. Ara-mony, 88 F.3d at 1382. The government relied on the following specific-items evidence.

First, Moore employed a “dance-watcher,” whose responsibility was to tally the number of lap dances each dancer performed each night. With this information Moore sought to ensure that each dancer turned over Moore’s cut of each lap dance fee, and also to enforce his minimum-dance requirement, under which a dancer who failed to perform a certain number of dances paid him a “fine.” During the February 2008 raid of the Club, the RPD seized (and later turned over to the IRS) dancewatcher notebooks for July and August 2005, and December 2007 through February 2008. Some pages tallied the number of dances performed, some showed dancers’ hours, and others tracked fines the dancers owed and/or paid.

Rager analyzed these notebooks to determine how much the Club likely earned from lap dance fees and fines during the periods covered by the notebooks. She then compared those totals with the revenue numbers Moore reported to Jonson. Rager testified that, according to her analysis, Moore substantially understated the Club’s revenue for the periods covered by the notebooks. In particular, the evidence showed at least the following:

She also testified that Moore received additional income during those periods, such as minimum-dance fines. Minimum-dance fines, she testified, increased the unreported income by $17,190 for July 1, 2005 through August 10, 2005, and $24,300 for December 1, 2007 through February 22, 2008. The government argues that the jury could reasonably extrapolate from that evidence, and thereby infer from Rag-er’s testimony, that Moore understated the Club’s gross receipts for each of tax years 2005 through 2007.

Second, the three dancewatchers who testified at trial examined a summary of the receipts reported from 2005 through 2007 for Thursdays, Fridays, and Saturdays, the Club’s busiest nights. All of them testified that the fines, lap dance fees, and cover charges reported on the daily sheets for the periods they worked at the Club were too low. They reached this conclusion because, for example, lap dance fees reported were lower than the cover charges reported, even though in their experience the Club took in more revenue from lap dances than from cover charges, and because the reports showed many nights when no fines were reported, even though fines were collected nearly every night.

Third, the government showed that although Moore collected cash advance fees from patrons, he never told his accountant he collected such fees.

Fourth, the government showed that Moore altered records to conceal his un-derreporting. In one instance, when an employee completed a daily sheet reporting cover charges of $2,395, Moore crossed out that figure and replaced it with $890; but $890 in cover charges was too low for that day, which was a busy weekend day. Moore also instructed Jonson to increase the fines and lap dance fees he had reported on the daily sheets for January 2008 after the dancewatcher notebook covering that month was seized during the search of the Club. On February 29, 2008, one week after the search, the amounts of gross receipts shown on the Club’s January 2008 books for fines and lap dance fees, and cover charges were increased by $35,520 and $5,280, respectively.

Fifth, in a will Moore signed on March 14, 2007, Moore attested that if the Club were run by a “competent manager,” it would net over $1 million per year. J.A. 1932. The government argued that because this number was far higher than the $546,887 and $688,304 he reported as gross receipts for 2005 and 2006 (and higher than the $808,470 on his unfiled draft 2007 return), Moore’s admission in- his will was further evidence that Moore was underre-porting his income.

Based on these specific items of evidence, the government argues that the evidence was sufficient for the jury to find that Moore willfully understated the Club’s gross receipts from 2005 to 2007 in two ways: (1) by understating the amount the Club received in the form of cover charges, lap dance fees, and dancer fines; and (2) by failing to report income at all in certain categories, such as cash advance fees, even though on the daily sheets there were blank spaces for Moore to include additional revenue sources.

We agree that the specific-items evidence, standing alone, was sufficient to support the verdicts on each count. From that evidence, the jury could reasonably infer that Moore willfully understated the Club’s gross receipts for 2005, 2006, and 2007. Nevertheless, because a primary focus of the trial was on the government’s bank-deposits evidence, we proceed to examine the sufficiency of that evidence, as well.

B.

The government also relied on a modified version of the bank-deposits method of proof, supplemented and corroborated by the specific-items evidence. The object of the bank-deposits method is to sum the deposits to a taxpayer’s account in a particular year, ascertain the portion of those deposits that constitutes taxable income, and then show that actual taxable income was higher than the reported taxable income.

The government’s burden under the bank-deposits method encompasses three elements: “(1) that, during the tax years in question, the taxpayer was engaged in an income producing business or calling; (2) that he made regular deposits of funds into bank accounts; and (3) that an adequate and full investigation of those accounts was conducted in order to distinguish between income and non-income deposits.” Abodeely, 801 F.2d at 1028. Once the government has established these elements, “the jury is entitled to infer that the difference between the balance of deposited items and reported income constitutes unreported income.” Id.

On the “adequate and full investigation” prong, which the Boulet court referred to as the “purification” prong, 577 F.2d at 1167, the government’s burden is to show that it did “everything that is reasonable and fair [in] the circumstance to identify any non-income transactions and deduct them from total deposits,” Abodeely, 801 F.2d at 1024-25 (alteration in original). “[T]he government is not required to negate all possible non-income sources of the deposits, particularly where the source of the income is uniquely within the knowledge of the taxpayer.” United States v. Slutsky, 487 F.2d 832, 841 (2d Cir.1973). “At the same time, however, the government may not disregard explanations of the defendant reasonably susceptible of being checked.” Id. (internal quotation marks omitted). “The critical question is whether the government’s investigation has been sufficiently adequate to support the inference that the unexplained excess in receipts was in fact attributable to currently taxable income.” Id.

If a particular deposit is from a nontaxable source (e.g., a transfer from another of the taxpayer’s bank accounts), then the government must deduct the amount of the deposit from the gross deposit figure. If (1) the government cannot identify the source despite all reasonable efforts to do so, (2) the defendant does not explain why the deposit did not constitute taxable income, and (3) the government proves that the failure to report the income was willful, then the jury may infer that the defendant willfully understated his income. See Slutsky, 487 F.2d at 840.

In this case, the government made three modifications to the typical bank-deposits analysis. First, ordinarily the government seeks to prove both the amount of unreported income that a defendant deposited in a bank and the amount of cash the defendant spent without ever depositing. See Boulet, 577 F.2d at 1167 (describing the latter as “the amount of expenditures made in cash”); Abodeely, 801 F.2d at 1023 (explaining that the phrase “cash expenditure” as an “adjunct to ‘bank deposits’ ” is a misnomer, and is more accurately described as “non-deposits”). Here, apparently for simplicity’s sake (and because it resulted in a more conservative estimate), the government limited its estimate of Moore’s unreported income to funds that were deposited, in one way or another, in the Club’s bank account.

Second, ordinarily in a bank-deposits case, the government seeks to show the total deposits for a full tax year in order to capture the defendant’s full actual income for that year. Here, as to 2005, again apparently for simplicity’s sake, the government limited its analysis to the period beginning July 28, 2005, the date Moore had the three ATMs installed in the Club.

Third, the government modified how it used the bank-deposits method. Ordinarily, the object of applying this method is to determine a taxpayer’s total corrected taxable income. Here, the existence of the ATMs in the Club, and the fact that the cash used to fund the. ATMs consisted solely of cash earned from operations at the Club, allowed the government to use the bank-deposits evidence in a different way. The government’s goal was to show that the Club must have received significantly more cash revenue than Moore reported as part of the Club’s gross receipts. At trial, the government alleged that in order to fund the ATMs, the Club must have received additional cash from an “unknown source” in the amounts of $104,958 in 2005, $497,095 in 2006, and $364,934 in 2007.

By the time of sentencing, the government conceded an error, and reduced the unreported gross receipts number for sentencing purposes to $34,400 for 2005, $368,457 for 2006, and $255,508 for 2007. Setting aside those recalculations for sentencing, Moore argues there was a significant flaw in the government’s proof at trial such that he is entitled to a judgment of acquittal on Count One and a new trial on Counts Two and Three.

As part of the government’s proof at trial, one element of its case was to show it had undertaken an “adequate and full investigation,” Abodeely, 801 F.2d at 1023, to determine Moore’s July 29, 2005 cash on hand. The July 2005 eash-on-hand figure was crucial because if Moore had substantial cash on hand as of the date the ATMs began operation, then the jury could not find that the cash used to fund the ATMs came from cash generated by operations at the Club.

To prove that Moore did not have a significant cash hoard as of July 2005, the government relied on the following evidence. On December 6, 2004, Moore generated a financial statement that listed his assets and liabilities, including cash on hand. In that financial statement, Moore represented that his cash on hand and in banks was $385,000. Rager corroborated this figure by examining bank records, real estate transactions, loans, safe deposit box records, and currency transaction reports (“CTRs”). She then subtracted the total balance in Moore’s bank accounts as of that date, which left $223,869 as the amount of actual cash Moore had on hand on December 6, 2004. From that amount, she subtracted the total in cash deposits Moore made to the bank between December 6, 2004, and July 28, 2005, which resulted in $96,803 in cash on hand as of July 28, 2005. This amount was less than $2,000 shy of the amount of cash Moore was discovered to have when the Club was searched in February 2008. Accordingly, the government’s evidence tended to show that although Moore had some cash on hand as of July 25, 2005, in effect he did not use any of it to fund the ATMs because he possessed virtually the identical sum of cash seven months later.

In the course of establishing Moore’s July 2005 cash-on-hand figure, the government presented evidence of funds that Moore withdrew from several safe deposit boxes, and then deposited in the L.A. Diner bank account. Moore argues, and apparently the government does not dispute, that the government’s evidence showed that from 1999 through the first half of 2005, he withdrew $359,000 in cash from safe deposit boxes and deposited it in the L.A. Diner account.

As the centerpiece of his appeal, Moore argues that this $359,000 represents capital contributions to the Club. That is, the money in the safe deposit boxes constituted Moore’s savings (either from pre-2005 income or from a substantial inheritance he received when his parents died), and thus did not constitute income taxable between 2005 and 2007. When (during the period before August 2007) he took that cash from safe deposit boxes and deposited it in the L.A. Diner account, Moore argues, he was making loans to the business. Thus, Moore essentially argues that because he loaned the business $359,000 pri- or to August 2005, and because the Club was a sole proprietorship, when the Club started generating profit after July 2005, he was entitled to offset the first $359,000 in income as a kind of credit.

This $359,000 offset, Moore argues, entitles him to a judgment of acquittal on Count One, because $359,000 is larger than the amount of alleged unreported income for 2005. He argues further that the government’s failure of proof also entitles him to a new trial on Counts Two and Three, because “errors of such magnitude would have materially aided the defendant’s argument that the government made hundreds of thousands of dollars in mistakes ... and that the defendant was not willful.” Moore Br. 26.

Moore’s argument is singularly unpersuasive. An owner of a sole proprietorship has no duty to document capital contributions to the business because such contributions have no tax consequences. Instead, the owner contributes whatever funds might be necessary to run the business, and the business and the owner are treated as a single entity for tax purposes and are liable for taxes on net income (i.e., gross receipts minus deductible business expenses). See Schedule C, IRS Form 2040; Littriello v. United States, 484 F.3d 372, 375 (6th Cir.2007) (noting that in a sole proprietorship, “a single individual owns all the assets, is liable for all debts, and operates in an individual capacity”). But Moore does not argue that he claimed (or would have claimed) the $359,000 as deductible business expenses, or that the money should be viewed as such. Rather, in Moore’s view, any capital contributions to a sole proprietorship, no matter how long ago they were made, can be used to offset a future tax liability from current income produced by the sole proprietorship. That is not the law, and Moore cites no authority to support his view that a sole proprietor can make loans to himself in this way and deduct future “loan repayments” whenever doing so suits the taxpayer.

In short, the amount Moore contributed to the business from 1999 through July 2005 is irrelevant to whether income the Club received after July 2005 constitutes taxable income to Moore. The evidence was thus sufficient for a jury to convict Moore based on the bank-deposits method of proof, as well as the specific items method of proof.

III.

Moore also seeks a new trial based on newly discovered evidence. He argues that, at trial, the government’s bank-deposits analysis overstated his taxable income for 2005 through 2007 by $191,236 because he had paid that amount in local and state taxes but did not deduct that amount from gross receipts. By the time of sentencing the government agreed that Moore should be credited with these payments, but at trial it had admitted only that the number should be decreased by about $92,000. Moore argues that Agent Rager’s eventual concession at sentencing that the original calculation of Moore’s unpaid tax liability was incorrect constituted newly discovered evidence, entitling him to a new trial. We disagree that this development merited a new trial.

Federal Rule of Criminal Procedure 33 states that a district court “may vacate any judgment and grant a new trial if the interest of justice so requires,” and describes “newly discovered evidence” as a potential reason for a new trial. “We review the district court’s Rule 33 decision for abuse of discretion.” United States v. Robinson, 627 F.3d 941, 948 (4th Cir.2010). In analyzing whether newly discovered evidence requires a new trial, we look to five factors:

(a) the evidence must be, in fact, newly discovered, i.e., discovered since the trial; (b) facts must be alleged from which the court may infer diligence on the part of the movant; (c) the evidence relied on must not be merely cumulative or impeaching; (d) it must be material to the issues involved; and (e) it must be such, and of such nature, as that, on a new trial, the newly discovered evidence would probably produce an acquittal.

Id. (quoting United States v. Custis, 988 F.2d 1355, 1359 (4th Cir.1993)).

Moore argues that Rager’s failure to concede her erroneous failure to credit Moore with the unclaimed deductions for state and local taxes was newly discovered evidence, because she did not make the concession until after Moore was convicted. Moore argues he was diligent in pursuing this “evidence” because his counsel vigorously cross-examined Rager, and recalled Jonson (who had testified for the government but then agreed that the government’s calculation was off by $191,236). Moore argues that had Rager admitted the error earlier, “there is a substantial likelihood that the jury would have viewed the government’s evidence differently, would have viewed the IRS agent’s testimony differently, and [would have] found that reasonable doubt existed on the tax counts.” Moore Br. 21.

The government responds that Moore’s claim fails because the concession at sentencing (1) was not newly discovered evidence; (2) was merely cumulative or impeaching; and (3) would not have impacted the verdict.

We need not decide whether Rag-er’s testimonial admission at sentencing constitutes “newly discovered evidence” for purposes of Rule 33 because Rager’s concession was “merely cumulative or impeaching,” and we cannot say that had the jury heard it, the testimony would have “probably produce[d] an acquittal.” See Custis, 988 F.2d at 1359. First, the jury heard testimony that Rager’s calculation was erroneous from one of the government’s own witnesses: Moore’s accountant, Jonson. Thus, Rager’s concession would have been cumulative. Second, even accounting for the adjustment for local and state taxes, Moore still under-reported his gross income for each of the years in question. Third, the government’s bank-deposits analysis was conservative; it assumed that cash on hand of any denomination was available to fund the ATMs, even though the ATMs only dispensed $20 bills, and it did not attribute any income to Moore for personal cash expenditures, though the bank-deposits method permits the government to include such expenditures. See, e.g., Boulet, 577 F.2d at 1167.

We thus reject Moore’s argument that the district court abused its discretion in denying the motion for a new trial based on Rager’s delayed concession that Moore should have been credited with $191,236.

IV.

Moore next argues that, even if there was sufficient evidence to support the verdicts, the district court committed reversible error in instructing the jury on how to apply the bank-deposits analysis. As explained above, the bank-deposits method requires that the government prove, among other things, how much cash Moore had on hand at the beginning of the relevant time period. Here, the time period the government used began on August 5, 2005, the date the ATMs became operational. Moore argues this was error. If the government wanted to use the bank-deposits method, he argues, the jury still had to be instructed “that the starting point for a cash-on-hand analysis was January 1, 2005.” Moore Br. 38. By shifting the starting date, he argues, the government inflated his unreported income by over $100,000. We disagree.

This argument reflects a misunderstanding of the government’s method of proof. By choosing August 5 as a starting point for 2005, the government sought to prove Moore’s unreported income only for the latter five months of 2005, not the full year. Because the government was starting its analysis of Moore’s bank deposits in August, that was the date it had to determine (and the jury had to find) Moore’s cash on hand. The reason for requiring proof of a beginning cash-on-hand figure is to determine whether and to what extent cash already in a defendant’s possession (rather than cash from taxable income) explains the source of a cash deposit during the relevant period. See, e.g., United States v. Mounkes, 204 F.3d 1024, 1028 (10th Cir.2000) (noting that proof of cash on hand is required to “distinguish between unreported, taxable income and those deposits and expenditures not derived from taxable income”).

As the government explains, because Rager’s bank-deposits analysis “relied exclusively on bank deposits attributable to ATM withdrawals to calculate the gross income defendant failed to report[,] ... only cash that defendant possessed on the date the ATMs were installed could offer an alternative explanation for the deposits to defendant’s bank account attributable to ATM withdrawals.” Gov’t Br. 34. In other words, Moore “could not have used any cash that he had on hand on December 31, 2004, to fund the ATMs unless he still had that cash on hand when the ATMs were installed.” Id.

The district court thus did not err in instructing the jury to determine Moore’s cash on hand as of August 5, 2005.

V.

Moore next argues that the district court erred in denying his motion to suppress. Before August 2007, the RPD was investigating Moore on suspicion that he was involved in narcotics and prostitution. The investigating officers came to suspect that Moore may have also been engaging in tax fraud, and in August 2007 contacted the IRS, asking it to assist in the investigation of Moore. On or about February 20, 2008, Ownby drafted a state search warrant. The City of Richmond Circuit Court issued the warrant on February 22, 2008. The government obtained the documentary evidence it introduced at trial during the execution of that warrant.

Moore argues that the search was unlawful for two reasons. First, he argues that the true purpose of obtaining a search warrant was to seize evidence that Moore was violating federal law, not state law; in his view, the state-law allegations in the warrant application were a pretext to allow the IRS to avoid obtaining a federal warrant, and the government therefore violated Federal Rule of Criminal Procedure 41. Second, he argues that the state warrant was overbroad and therefore violated the Fourth Amendment.

A. '

We first examine whether the search violated Federal Rule of Criminal Procedure 41. The Federal Rules of Criminal Procedure govern “criminal proceedings” in the federal courts. Fed.R.Crim.P. 1(a)(1). Rule 41 governs the process for applying for, obtaining, and executing a federal search warrant. Unless an exception to the warrant requirement applies, Rule 41 requires that investigating officers obtain a warrant issued by a federal magistrate judge, “or if none is reasonably available, a judge of a state court of record in the district.” Fed.R.Crim.P. 41(b)(1).

The evidence in this case was obtained during the execution of a state search warrant, in the context of an investigation that involved both state and federal agents. Moore argues that because federal agents were involved in preparing the search warrant application and in executing the search, Rule 41 applied. Because the Rule requires either that officers have obtained a federal warrant or that a federal magistrate judge have not been “reasonably available,” and because neither condition was met here, he argues the government violated Rule 41. Finally, he argues, the violation of Rule 41 justifies suppressing the evidence obtained during the execution of the warrant.

We addressed the applicability of Rule 41 to a joint federal-state investigation most recently in United States v. Claridy, 601 F.3d 276 (4th Cir.2010). There, the search was conducted pursuant to a state search warrant obtained by a state police officer who was part of a formal federal-state joint task force and had been federally deputized. Id. at 278. The defendant argued that the officer “violated Fed. R.Crim.P. 41 by applying to a state judge for a warrant, despite the fact that he was conducting a federal narcotics investigation and despite the fact that there was no indication that a federal magistrate was unavailable.” Id. at 279. We rejected that argument and devised the following test:

[T]he triggering condition for application of Rule 41 is not a finding that the investigation was federal in nature but a determination that the proceeding was a federal proceeding.... When ... federal and state agencies cooperate and form a joint law-enforcement effort, investigating violations of both federal and state law, an application for a search warrant cannot categorically be deemed a “proceeding” governed by the Federal Rules of Criminal Procedure, based simply on the role that federal law-enforcement officers played in the investigation. See, e.g., [United States v. Smith, 914 F.2d 565, 569 (4th Cir.1990) ] (observing that mere involvement of federal officers in the execution of the search warrants does not trigger application of Rule 41). Such an investigation is conducted on behalf of both sovereigns, and its object is to reveal evidence of crime — be it federal crime or state crime....
[Wjhen a member of a joint task force initiates a proceeding in state court to obtain a search warrant in furtherance of the joint investigation, it is not only relevant to understand the role of federal officers in obtaining the warrant and conducting the search, but it is also necessary to review the details of the proceeding itself to determine what law the warrant will serve and the scope of the warrant.

Id. at 281-82 (emphasis in original). The facts the Claridy court deemed material to finding that the “proceeding” for obtaining the search warrant was a state proceeding (governed by state law) rather than a federal proceeding (governed by Rule 41) were (1) the warrant application alleged violations of state law; (2) the officers authorized to execute the search were state officers; and (3) the warrant was returnable to the state court.

Here, it is undisputed that the same three facts are present. Nonetheless, Moore argues that the federal agents’ role in obtaining and executing the search warrant here was greater than in Claridy, for these reasons: (1) Rager opened a “primary” IRS investigation of Moore into money laundering to assist Ownby and track her time; (2) Rager analyzed Moore’s bank records to help Ownby prepare the search warrant application; (3) Rager’s time records showed that on February 20, 2008, she recorded six hours as “draft SW”; (4) in the warrant application, Ownby stated he had experience investigating violations of the federal Money Laundering Control Act, not any state money laundering statutes; (5) in an internal IRS form Rager prepared before executing the search, she referred to Moore’s income as “legal income,” which Moore argues suggests a federal tax case despite Rager’s testimony • that she had simply made an error filling out her form; (6) the majority of the officers present during the execution of the search warrant were federal (including 10 IRS agents and four other federal agents), and Rager’s IRS supervisor was listed on a “preop” report as a supervisor (though Rager indicated that this merely referred to a job classification rather than a role in the search); (7) after the search, although city agents reviewed seized videotapes, only IRS agents reviewed seized financial records; and (8) the local special prosecutor testified that the focus of her investigation was narcotics and prostitution, not money laundering.

Because Rager later opened an official federal investigation of Moore, and the financial records seized during the search were admitted at trial, Moore argues that the state money laundering offense was listed in the search warrant application “as a pretext to allow the IRS agent access to the financial records without seeking a federal search warrant under Rule 41.” Moore Br. 45.

The government responds that the district court did not clearly err in finding that the state law allegations were not a pretext for avoiding having to obtain a federal warrant, and therefore no federal warrant was required and Rule 41 did not apply. The government relies on the following countervailing evidence: (1) Rager testified that Ownby, a state officer, asked Rager to examine Moore’s bank records because of her expertise in financial investigations; (2) both Rager and Ownby testified that although Rager assisted with some analysis of Moore’s bank records for inclusion in the search warrant application, Rager did not otherwise assist in drafting or reviewing the warrant; (3) the warrant itself was issued to investigate only state crimes (narcotics, prostitution, public nudity, bestiality, and money laundering); (4) Ownby testified that he decided to include the state money laundering charge in the application because he wanted to investigate further what Moore was doing with the proceeds from the suspected drug dealing and prostitution, not to gather evidence of tax fraud; (5) the affidavit attached to the warrant application provided evidence of state crimes, not federal crimes; (6) Ownby, not Rager, was responsible for planning and executing the search of the Club; and (7) a member of Ownby’s unit took custody of the items seized in the search.

We agree with the government that the district court did not clearly err in finding that the IRS only assisted in the preparation and execution of the search warrant. There was sufficient evidence for the district court to find that, under Claridy, Rule 41 did not apply and thus the allegations of state law were not a pretext for avoiding having to obtain a federal warrant. The district court therefore properly concluded that the absence of a federal warrant did not render the search unlawful.

Moore argues Claridy is distinguishable because the IRS and the RPD did not have a formal joint investigation arrangement as existed in Claridy. But that is not a meaningful distinction. In Claridy, it was not the structure of the investigation that determined the law that applied to the issuance of the warrant, but the proceeding the law enforcement officers chose to pursue to obtain the warrant. 601 F.3d at 281-82. Moreover, the existence of the task force in Claridy cuts against Moore’s argument, because the federal government’s role in the investigation in Claridy was more extensive than the IRS’s role here. See also United States v. Williams, 977 F.2d 866, 867, 869-70 (4th Cir.1992) (holding Rule 41 did not apply because there was “no evidence suggesting that the warrant obtained by [a state police officer] was issued in response to a directive or urging from” a federal agent); United States v. Smith, 914 F.2d 565, 569 (4th Cir.1990) (holding Rule 41 did not apply because there was “no evidence that [the state police officer] applied for the warrant at the direction or urging of a federal officer”).

B.

We next examine whether the warrant was overbroad. The Fourth Amendment requires that a search warrant “particularly describ[e] the ... things to be seized.” U.S. Const, amend. IV. The warrant here authorized officers to search and seize a wide range of materials, including “[a]ny and all bank records” and all “items evidencing the obtaining, secreting, transferring, and/or concealment and/or expenditure of money.” J.A. 127. Moore argues that, as to the financial records to be seized, the warrant was insufficiently particularized because it “set no temporal limit” on which such records could be seized, even though “the allegations that formed the basis for the affidavit described events occurring in 2006 and 2007.” Moore Br. 45.

We disagree. When “[t]he dates of specific documents could not have been known to the Government,” a search warrant need not be limited by “specific time periods.” United States v. Shilling, 826 F.2d 1365, 1369 (4th Cir.1987) (abrogated on other grounds by Staples v. United States, 511 U.S. 600, 114 S.Ct. 1793, 128 L.Ed.2d 608 (1994)). Moore has pointed to no evidence showing that officers had reason to believe his alleged money laundering was limited to particular years. Though officers had Moore’s general bank account information, they could not have known what specific documents revealing money laundering (or other financial crimes) Moore possessed, what years they corresponded to, or what years (if any) would suggest money laundering. Further, where fraud is concerned, there is leeway to allow for more expansive warrants. See, e.g., United States v. Oloyede, 982 F.2d 133, 139-140 (4th Cir.1992).

At bottom, the warrant was concerned, in part, with “financial records that, by their nature reveal an attempt to disguise and conceal the true nature of a prostitution business,” J.A. 127. Consequently, the officers had no way of knowing the specific time periods of those records. As a result, we hold that the district court did not err in evaluating the sufficiency of the warrant’s particularity.

VI.

Moore next argues that the district court erred when it excluded the following evidence: (1) exhibits showing Club income for 2009 and 2010; (2) impeachment evidence that several of the Club’s former employees failed to file tax returns; and (3) evidence that Moore’s accountant advised him not to file a tax return in 2007. “We review a trial court’s rulings on the admissibility of evidence for abuse of discretion, and we will only overturn an evidentiary ruling that is ‘arbitrary and irrational.’ To that end, we ‘look at the evidence in a light most favorable to its proponent, maximizing its probative value and minimizing its prejudicial effect.’ ” United States v. Cole, 631 F.3d 146, 153 (4th Cir.2011) (citations omitted).

A.

We turn first to Moore’s argument that the district court abused its discretion in excluding exhibits showing Club income for 2009 and 2010. As explained above, the government’s specific-items method of proving Moore’s unreported income included use of the recovered dancewatcher notebooks, which contained records for just a few months, to determine a monthly average from which to extrapolate the yearly unreported income. At trial, Moore argued that this method overstated his actual income because the months for which there were dancewatcher notebooks happened to be particularly lucrative.

One way Moore sought to substantiate his position was through income statements that Jonson prepared for 2009 and 2010, based on the daily sheets Moore provided him during those years. He argued those documents were relevant because they provided “some probative value in determining whether there was consistency in the dollars that [Moore] reported” on the daily sheets. J.A. 1201. In other words, the income Moore reported to Jonson in 2009 and 2010 would give the jury “a more complete picture of whether there is, in fact, underreporting or whether the reporting is consistent.” J.A. 1203. This evidence, he argued, showed that the Club’s income averaged $12,000 to $17,000 per month both before the February 2008 search and after — not the higher amount argued by the government.

The government objected, on what seems to have been two grounds. First, the government argued the 2009 and 2010 statements were irrelevant to the Club’s income from 2005 to 2007, the tax years in question. Moreover, even if Moore’s reported income for 2009 and 2010 was similar to his reported income in 2005 to 2007, that was irrelevant to the amount of his unreported income in 2005 to 2007. In other words, the amount Moore put on the daily sheets in any of the years was irrelevant to how much he failed to include on those sheets. Second, the government argued that, to the extent the evidence was relevant, there was no foundation for it. The statements would only have been relevant to the amount of Moore’s unreported income for 2005 to 2007 if the 2009 to 2010 statements, unlike the daily sheets from previous years, included all of the Club’s income. To establish relevance on that basis, Moore had to show that there was a change in procedure around 2008, such that Moore began reporting all of the Club’s income on the daily sheets. Moore sought to lay such a foundation through Jonson, but could not do so because Jonson lacked firsthand knowledge about Moore’s reporting practices, and his testimony on that point was thus hearsay.

The district court sustained the government’s objection on Rule 403 grounds. The court first explained that Moore had failed to lay a foundation for the income statements, and that in any event the documents had “marginal relevance ... if any.” J.A. 1206. Moreover, to the extent the documents were marginally relevant, their relevance was “outweighed by delay and confusion”: delay because of the time “necessary to deal with it,” and confusion because “the jury likely would be. having to guess what the foundation for the document was.” Id.

On appeal, Moore argues the court’s foundation ruling was wrong because one of the government’s own witnesses testified that “the post-search procedure was to record all dance income in the cash register (which insured the accountant would pick it up on the tax return).” Moore Br. 27 (citing J.A. 667-68). Moore also argues that the statements were admissible “even without that foundation, since [he] knew, post-search, that he was under investigation and had an incentive to report his income or risk more charged offenses.” Moore Br. 27-28 (citing J.A. 682-83).

We hold that the district court did not abuse its discretion in excluding the income statements from 2009 and 2010. The court acted well within its discretion in concluding that their relevance was outweighed by delay and the risk of confusion.

B.

We next turn to Moore’s argument that the district court erred in excluding impeachment evidence concerning several of the government’s witnesses who were former Club employees. At trial, the government stipulated that three of its witnesses filed tax returns that were false because they did not report cash tip income. The court permitted Moore to cross-examine those witnesses about their allegedly false returns, on the ground that making a false statement on a tax return is evidence of untruthfulness, and therefore can be used to impeach a witness under Federal Rule of Evidence 608(b).

Moore also sought to cross-examine three other former Club employees about their failure to file tax returns at all. He argued that their failure to file was as relevant to truthfulness as the filing of false returns, because “[i]f you don’t file your tax return, it could be a crime.” J.A. 797. The district court sustained the government’s objection on Rule 403 grounds. The court explained that a person’s failure to file a tax return is not necessarily evidence of untruthfulness, because there might well be an innocent explanation for the failure to file. A failure to file serves to impeach a witness only if “the circumstances surrounding the failure to file” prove that the witness actually owed taxes. J.A. 797. If Moore were to ask the former employees whether they filed returns, that question would have “opened the door to testimony about the reasons why the former employees failed to file returns, thereby potentially confusing the jury about the issues and delaying the trial.” J.A. 1351. Accordingly, the court reasoned that “failing to file a tax return was not probative of character for untruthfulness, and, to the extent that it might be minimally relevant, the marginal relevance was substantially outweighed by the danger of confusion of the issues, misleading the jury, and considerations of delay and waste of time under Rule 403.” Id.

On appeal, Moore argues that the court abused its discretion in so concluding. We disagree. Moore is correct that the witnesses’ conduct could have been not only a misdemeanor failure to file, but also felony tax evasion. But the witnesses’ failure to file would have been relevant only if they owed taxes, and establishing that fact would have required substantial time and effort. The court properly exercised its discretion in finding that to the extent the witnesses’ failure to file was relevant to their character for truthfulness, the delay and confusion in establishing that fact outweighed any impeachment value.

C.

We turn now to Moore’s argument that the district court abused its discretion in refusing to admit evidence that Moore’s accountant advised him not to file a tax return in 2007. Moore’s tax return for 2007 was originally due April 15, 2008, and October 15, 2008, with extensions. He had made $60,000 in estimated tax payments during 2007, including $50,000 in estimated federal income taxes. In October and November 2008, he made two additional tax payments totaling $95,000 for tax year 2007. But he never filed a return for 2007.

Count Three charged that Moore committed tax evasion in violation of 26 U.S.C. § 7201 because he “received taxable income of approximately $718,398.54” and thus owed “a substantial amount of income tax,” but “willfully attempt[ed] to evade and defeat a large part of the income tax,” in part by committing the following “affirmative aet[s] of evasion”:

(a) maintaining a double set of books and records for CLUB VELVET;
(b) self-funding CLUB VELVET’S ATM machines with substantial amounts of unreported cash proceeds; and
(c) providing [Jonson] with false financial information regarding CLUB VELVET’S gross cash receipts.

J.A. 150-51.

As stated above, the three elements of a violation of § 7201 are (1) willfulness, (2) a substantial tax deficiency, and (3) “an affirmative act constituting an attempted evasion of the tax.” Goodyear, 649 F.2d at 228. At trial, to prove that his failure to file a return for 2007 did not constitute a willful attempt to evade taxes, Moore sought to offer Jonson’s testimony that Jonson was told by Moore’s attorney not to file the 2007 return, given the pendency of the criminal case.

Although Moore frames his argument as an evidentiary issue, it appears more like an argument asserting legal insufficiency. He does not seem to dispute that his failure to file was “willful” in the sense that he fully intended not to file. Rather, he seems to argue that the government must also show that the failure to file itself constituted an act of tax evasion. But the government did not allege, or argue at trial, that the failure to file was an “affirmative act of evasion.” The statute requires proof of “evasion” only as to those alleged acts. Accordingly, absent a reliance-on-counsel defense (which Moore did not raise), the reason he failed to file (i.e., advice of counsel) was irrelevant to the government’s case or any cognizable defense, and thus the district court properly excluded that evidence.

Further, to the extent the jury might otherwise have been confused and believed that failure to file alone could constitute evidence of an affirmative evasive act, the court’s instruction was adequate to clear up any such confusion. That instruction included the following:

[T]he phrase “attempts in any manner to evade or defeat any tax” contemplates and charges that Mr. Moore knew and understood that during the calendar year 2007, he owed a substantial federal income tax, and that he tried in some way to evade that tax.
I instruct you now that merely failing to file a return is not sufficient to establish an attempt to evade a tax. You may not draw any adverse inference from the fact that the defendant did not file an income tax return for 2007.

J.A. 1318 (emphasis added). In these circumstances, we cannot hold that the district court abused its discretion in refusing to allow Jonson to testify that Moore’s attorney told him not to file the 2007 return.

VII.

Moore also raises two issues concerning his sentence. First, he asserts that the district court clearly erred in finding a tax loss greater than $400,000 at sentencing. Next, he asserts that the district court abused its discretion in imposing a $250,000 fine.

A.

We turn first to Moore’s argument concerning the district court’s finding of a tax loss greater than $400,000. The applicable sentencing guideline provides standards for “Tax Evasion; Willful Failure to File Return, Supply Information, or Pay Tax; Fraudulent or False Returns, Statements, or Other Documents.” U.S.S.G. § 2T1.1. Subsection (a) establishes the base level for the offense according to the amount of “tax loss,” or designates the level as 6 if the crime caused no tax loss. U.S.S.G. § 2T1.1 (a). Subsection (c)(1) explains that “[i]f the offense involved tax evasion or a fraudulent or false return, statement, or other document, the tax loss is the total amount of loss that was the object of the offense (i.e., the loss that would have resulted had the offense been successfully completed).” U.S.S.G. § 2Tl.l(c)(l). Note (A) to subsection (c)(1) establishes the following formula for computing tax loss in cases involving fraudulent filings: “28% of the unreported gross income ... plus 100% of any false credits claimed against tax, unless a more accurate determination of the tax loss can be made.” U.S.S.G. § 2Tl.l(c)(l) n.(A).

Under the Guidelines, the government must prove tax loss by a preponderance of the evidence. United States v. Butner, 277 F.3d 481, 487 (4th Cir.2002). However, “[t]he amount of tax loss is not always a precise figure, and ‘the guidelines contemplate that the court will simply make a reasonable estimate based on the available facts.’ ” United States v. Mehta, 594 F.3d 277, 282 (4th Cir.2010) (quoting U.S.S.G. § 2T1.1, cmt. n. 1). “In assessing whether a district court has properly applied the Guidelines ... we ‘review the district court’s legal conclusions de novo and its factual findings for clear error.’” United States v. Manigan, 592 F.3d 621, 626 (4th Cir.2010) (citation omitted). “Generally, the district court’s calculation of the amount of loss for sentencing purposes is a factual finding reviewed for clear error.” Mehta, 594 F.3d at 281.

At sentencing, the government presented two alternative ways to calculate the tax loss: a “conservative” method, which yielded a loss of $321,000, and an “aggressive” method, which yielded a loss of $458,606. Moore objected to both, and the district court adopted the latter.

The first method, which resulted in the more “conservative” loss of $321,000, was a reiteration of the government’s modified bank-deposits analysis at trial, although it credited Moore with sales and admissions taxes the Club had paid from 2005 to 2007. This analysis, which was modified to limit deposits to those attributable to ATM withdrawals, yielded a loss of $321,676. That was the number adopted by the Probation Office in its pre-sentence investigation report. Moore argues that this calculation was erroneous because “the IRS[] fail[ed] to credit Moore with the approximate $359,000 in deposits he made to the business before 2005.” Moore Br. 47 n. 7. This argument fails for the same reasons the $859,000 in pre-2005 deposits could not offset taxes due on income the Club received later.

The government’s second calculation was more aggressive, and yielded a loss of $458,606. The government reached this figure by extrapolating from the five months of records contained in the dance-watcher notebooks. Leaving out some additional potential sources of income, the government calculated that in these five months, the total unreported income was $96,988 in lap dance fees and recorded fines, and $51,030 in minimum dance fines. This produced a monthly average of $19,416 in unreported lap dance fees and recorded fines, and $10,206 in unreported minimum dance fines. The government then multiplied these average numbers by the number of months between March 2005 and February 2008 for which there was no dancewatcher data, and added to the unreported income amounts for the five months for which data existed. This produced a 36-month total of $1,065,742 in unreported income. The government then calculated the total federal and state tax loss from 2005 to 2007 by adding the $1,065,742 in unreported income to the income Moore reported on his 2005, 2006, and draft 2007 returns, and then calculating the resulting additional tax due. This resulted in a total tax loss of $458,606.

Moore argues that this analysis suffered from five flaws, but we are not persuaded by his arguments. First, Moore argues that “the data sample was too small.” Id. Moore is correct that the government relied only on dancewatcher notebook tallies from July 2005, 10 days in August 2005, December 2007, January 2008 and part of February 2008, and then extrapolated the data from those five months to the remaining 31 months. But this was a reasonable methodology, especially because the government expressly excluded several categories of income in order to err on the side of underestimating Moore’s unreported income.

Second, Moore finds error in the fact that part of the sample was from January and February 2008, rather than the years for which Moore was prosecuted. This argument erroneously assumes that there was something about January and February 2008 that rendered the Club’s income non-probative of the Club’s pre-2008 income. There was nothing inherently wrong about using dancewatcher tallies from 2008 to estimate the Club’s monthly income in previous years.

Third, Moore argues that the income in some of the months included in the calculation was not representative, and that the government should have included data from 2008 to 2010. But Moore has not shown that the district court’s adoption of the government’s calculation was clearly erroneous. Similarly, the court did not clearly err in declining to consider income amounts for the remainder of 2008. As the government explains, “the trial evidence showed that the change in defendant’s reporting practices was the result of the search of Club Velvet and, moreover, even though the amounts defendant reported increased, business volume actually declined following the search.” Gov’t Br. 52.

Fourth, Moore argues that the government’s method of proof erroneously failed to deduct from his gross income certain business expenses, namely cash payments to waitresses, dancers, cover charge collectors, and doorwatchers. Although he did not claim these as deductions on his tax returns, he argues the district court erred in failing to deduct these expenses in calculating his total taxable income for sentencing purposes. The government offers two arguments in response. First, the government argues Moore’s position is “unsupported by the record” because Moore “fails to point to any evidence demonstrating the timing or amount of these purported cash expenditures.” Gov’t Br. 53. Second, in reliance on United States v. Delfino, 510 F.3d 468 (4th Cir.2007), the government argues that “the district court was not required to consider any deductions attributable to cash expenditures that [Moore] never claimed on a filed tax return.” Gov’t Br. 53.

If the district court had to take into account potential, but unclaimed, deductions, the burden is on Moore to prove he was entitled to those deductions. United States v. Gordon, 291 F.3d 181, 187 (2d Cir.2002). Thus, Moore is arguing (1) as a legal matter, tax loss must account for unclaimed but proven deductions, and (2) he met his burden to show that he was entitled to deduct from his gross income cash he paid to employees. The government responds that (1) as a legal matter, a taxpayer convicted of tax evasion or filing a false return is not entitled to unclaimed deductions in calculating tax loss under U.S.S.G. § 2T1.1, and (2) even if tax loss should be reduced by the amount of unclaimed deductions, Moore did not prove he was entitled to any unclaimed deductions for cash paid to employees.

Moore’s argument is mostly, but not entirely, foreclosed by Delfino. There, however, the defendants did not file any tax returns, whereas Moore filed tax returns for 2005 and 2006, and for most purposes the government treated Moore as if he had also filed a tax return for 2007. We decline to determine whether this distinction renders Delfino distinguishable, because Moore’s claim fails for another reason: he has not presented any evidence demonstrating the timing or amount of the expenditures purportedly giving rise to unclaimed deductions. In other words, Moore failed to prove he was entitled to a deduction (albeit unclaimed) for business expenses based on cash expenditures to dancers and other employees.

Fifth and finally, Moore argues that the government failed to reduce the alleged unreported income by the $359,000 in deposits he made from his personal account to the L.A. Diner account. This argument fails for the reasons discussed above.

The district court thus did not err in finding a tax loss greater than $400,000.

B.

Moore also challenges his fine. At sentencing, the government sought, and the court adopted, a two-level upward departure to a guideline level of 24. For this offense level, the advisory fine range was $10,000 to $100,000. U.S.S.G. § 5E1.2(c)(3). The district court imposed a variant fine of $250,000. Moore argues the fine was “excessive and not justified by the record,” and in any event the district court imposed the fine “without sufficient explanation.” Moore Br. 54.

We disagree with Moore. First, the district court’s explanation was sufficient. In explaining its decision to vary upward under 18 U.S.C. § 3553(a), the court stated that the increased fine was necessary “to reflect the seriousness of the offense, including the loss here, and to promote respect for the law and promote just punishment and afford deterrence.” J.A. 1548. The court also noted that Moore’s offense was particularly serious, justifying an above-Guidelines fine, because (1) Moore “engaged in a deliberate, calculated scheme”; (2) “he did it in a way that lasted over a substantial period of time”; (3) “he tried ... to imbue [his scheme] with legitimacy by using his accountant and misleading his accountant into what the income was”; (4) he “engaged in some of the most obstructive behavior” that the court had seen; and (5) he engaged in that behavior “even while the case was proceeding to and during trial.” J.A. 1549-50. In the court’s view, Moore, “and anybody else who would be inclined to commit offenses such as this, need[ed] to be deterred from” committing such conduct. J.A. 1550. This was a satisfactory explanation for the upward variance on the fine.

Second, the evidence supported the district court’s finding that Moore engaged in “obstructive behavior.” First, Moore tried to influence Lauren Jennings, a former waitress and bartender at the Club who was subpoenaed to give grand jury testimony. She testified that Moore told her to lie to the grand jury and testify that she was paid by check, not in cash. Second, before trial the government showed that one of the witnesses the defense planned (but later declined) to call, Claire Coleman, a former Club dancer and dancewatcher, was receiving a “pretty penny” for testifying. Third, there was evidence that Moore tried to hide his assets. After learning of the indictment, Moore transferred his interests in the Club to a friend, Scott Staten, who sold the club to a third party but maintained the proceeds for Moore in an account under Staten’s name. Staten also sold four of Moore’s vehicles for him, maintaining the proceeds in the same manner.

Moreover, the fine was within the statutory maximum. Under 18 U.S.C. § 3571(d), the maximum fine is “twice the gross gain or twice the gross loss.” As discussed above, the district court did not clearly err or abuse its discretion in finding that the amount of the tax loss was over $400,000. A $250,000 fine obviously does not exceed twice that loss.

VIII.

For the reasons set forth, we affirm the judgment in all respects.

AFFIRMED. 
      
      . The overarching question at trial was whether the government proved that the Club's gross receipts were in fact substantially higher than the amount Moore reported on Schedule C of his Form 1040 tax returns.
     
      
      . The Club also received money that Moore invested from his own savings. Because the Club was a sole proprietorship, those funds did not constitute taxable income for the Club (since Moore was effectively transferring his own funds among his own accounts). Thus, any of Moore's own funds that he contributed to the Club (either in cash or to the Club's Bank of America account in the name of L.A. Diner) did not constitute taxable income.
     
      
      . Because the Club was a sole proprietorship, Moore reported the business's receipts or sales on Schedule C of his individual Form 1040 tax return. Counts One and Two therefore alleged that the amounts Moore reported as gross receipts or sales on his Schedule C returns were less than the actual gross receipts or sales.
     
      
      . At trial the government argued that the 2005 understatement was $101,953, but by sentencing decreased the estimated understatement to $34,400.
     
      
      . There is some confusion as to the amount that the government argues the 2007 receipts were understated. In its brief, the government asserts that unreported cash receipts for 2007 were $237,621, Gov’t Br. 16, but the sentencing exhibit it cites for the figure lists unreported receipts for 2007 as totaling $255,506, J.A. 1560. For purposes of this appeal, we assume the sentencing exhibit figure is the correct one.
     
      
      . The specific-items evidence was also relevant to the bank-deposits method of proof, because the specific-items evidence (such as ledgers tallying lap dances) corroborated that die funds deposited in the L.A. Diner account constituted income the Club received in the course of its business.
     
      
      . The affidavit described grand jury testimony from two undercover Virginia ABC agents and an informant who worked with the ABC agents that (1) Moore provided cocaine and heroin to Club employees; (2) a Club dancer sold cocaine to the second informant; (3) Ownby’s informant procured prostitutes from the Club, and Moore received a portion of the fee; (4) Club dancers regularly provided sexual services to patrons; and (5) Moore used the Club's surveillance cameras to videotape sexual acts performed there.
     
      
      . We do not reach the question of whether suppression would have been an appropriate remedy if a Rule 41 violation had in fact occurred.
     
      
      . Our conclusion is bolstered by the fact that, at trial, Moore argued simply that Jonson’s testimony provided the necessary foundation, and failed to make either of the arguments to the court that he now makes on appeal.
     
      
      . Moore also argues that by including February 2008 in its calculations, the government understated his reported income because the warrant was executed on February 23, 2008, and he had not yet reported that month’s income to the accountant. But as the govemment correctly points out, that fact is irrelevant because Moore had completed a daily sheet for each day in February prior to the search. The amounts he intended to report to his accountant were therefore apparent.
     
      
      . Moore claimed deductions only for those payments he made by check.
     
      
      . We review de novo whether "the tax loss includes deductions." Delfino, 510 F.3d at 472.
     