
    UNITED STATES of America, Appellee, v. Douglas G. RADTKE, Appellant. United States of America, Appellee, v. Scott Christopher Radtke, Appellant. United States of America, Appellee, v. Michael Thomas Donohoe, Appellant.
    No. 04-2587, 04-2593, 04-2611.
    United States Court of Appeals, Eighth Circuit.
    Submitted: Dec. 15, 2004.
    Filed: July 18, 2005.
    
      Counsel who presented argument on behalf of the appellant, Douglas G. Radtke, was Paul C. Engh, Minneapolis, Minnesota. Counsel who presented argument on behalf of appellant, Scott Christopher Radtke, was Donald M. Lewis, Minneapolis, Minnesota. Counsel who presented argument on behalf of the appellant, Michael Thomas Donohoe, was Robert Dino Sicoli, Minneapolis, Minnesota.
    Counsel who presented argument on behalf of the appellee was AUSA D. Gerald Wilhelm, Minneapolis, Minnesota.
    Before WOLLMAN, LAY, and COLLOTON, Circuit Judges.
   COLLOTON, Circuit Judge.

Douglas Radtke, Scott Radtke, and Michael Donohoe appeal their convictions for conspiracy to defraud the United States and the IRS, mail fraud, and federal tax law violations. They also appeal their sentences. We affirm.

I.

The appellants’ convictions resulted from their actions during the 1990s in connection with two corporations — Radtke Construction Company (“RCG”) and Scaffold Services, Inc. (“SSI”). Douglas Radtke incorporated RCC in 1971 to perform construction work for the Department of Housing and Urban Development. He bought SSI, a scaffolding supply company, in 1974. During, the 1990s, Douglas Radtke owned all of RCC and part of SSI, and was CEO of both companies. RCC was party to collective bargaining agreements with several unions, including the Carpenters and Joiners Union (“Union”). SSI was not party to any such agreements. Douglas Radtke’s son Scott Radtke was vice-president and minority owner of SSI. Michael Donohoe was a field operations manager with SSI.

Beginning in 1992, SSI and RCC began intermittently paying employees for services performed on an ad hoc basis with checks written directly from the companies’ “accounts payable” bank accounts, rather than through the companies’ payroll system. These checks, referred to by all parties as “cash checks,” withheld no taxes or union benefit payments. Until 1998, whether to pay an employee with a cash check or through the normal payroll system was decided on a case-by-case basis after the work had been performed.

In the early 1990s, Douglas Radtke hired Rita Galston to be SSI’s controller. She was promoted to chief financial officer in 1997. Galston testified at trial that she had believed at the time she worked for SSI that paying workers who were not “regular employee[s]” of the company (“casual workers”) without withholding taxes was permissible, so long as the payment amount did not exceed' $600 in any given year. Many of the cash checks used to pay SSI and RCC employees were approved by Galston. Because of the supposed $600 ceiling on the dollar amount of the cash checks, casual workers who received cash checks totaling more than $600 were paid in checks made payable to relatives or friends. When workers who were on the regular payroll of SSI or RCC were paid in cash checks, a substitute name was always used.

At trial, evidence was presented regarding specific instances in which cash checks were paid in these substitute names. Gal-ston testified that Douglas Radtke expressly authorized the use of cash checks to compensate his son Marc on two occasions. One time, the compensation was for driving a truck for SSI, and the check was made out in the name of Marc’s wife, Damita. The second cash check paid to Marc Radtke, according to Galston, was made out in the name of his mother, Diane Radtke. A former SSI employee testified that Scott Radtke told him to submit a social security number and name not his own in order to receive payment over $600. Donohoe acknowledged that he was paid several times with cash checks made out to persons other than himself.

In 1997 and 1998, the use of cash checks at SSI became more regular with respect to a particular project. SSI won a contract to provide scaffolds for an inspection and repair project at Hennepin Energy Resource Company (“HERC”) in 1997. The job at HERC involved a scaffolding system new to SSI. According to project manager Scott Such, Douglas Radtke, fearing it might take more time than expected to assemble the scaffolding, asked several workers including Such if they would be willing to receive payment in the form of cash checks for their work on the job. The savings SSI achieved through its non-payment of withholding taxes on the amounts paid by cash checks reduced the risk of a loss to the company on the HERC job.

SSI continued to perform services for HERC in 1998, but it became difficult to persuade workers to sign on for the “dirty, unpleasant job.” (D. Radtke Br. at 14). According to Galston’s testimony, Scott Such, the SSI project manager in charge of the HERC job, eventually approached her about the possibility of paying all of the workers at the job in cash checks as a means of persuading enough of them to participate. Galston believed that, because of the dollar amount of the HERC job (between $20,000 and $40,000 for labor in 1998), she could not authorize the use of cash checks for all of the workers without Douglas Radtke’s approval. She testified that she and Such approached Douglas Radtke with the proposal, and that she told him of the “upside and downside of paying cash on a job this size.” (T. Tr. at 290). The upside, according to Galston, was the savings to SSI despite compensating workers at a higher level. The downside of which Galston says she informed Douglas Radtke involved penalties and interest that would be assessed for SSI’s failure to pay taxes or union benefits on the employees’ pay, if the company’s actions were discovered.

Galston testified that she did not recall specifically informing Douglas Radtke that using cash checks would be “against the law,” (T. Tr. at 291), but claimed she told him that “from a risk standpoint, basically, one unhappy employee blowing the whistle would bring this to light.” (Id. at 292). According to Galston, Douglas Radtke thought about the proposal for between five and ten minutes before approving it, saying he “felt that his employees were loyal to him and that none of them would ... turn him in.” (Id.).

Galston’s testimony was not uncontro-verted at trial. Although Scott Such recalled discussing with Douglas Radtke the use of cash checks for himself and two other workers on the HERC project in 1997, he did not have any recollection of the April 1998 meeting recounted by Galston. Similarly, Douglas Radtke presented evidence indicating that he was traveling out of state during the time that Galston recalled meeting with him in April 1998.

After the 1998 HERC job, use of cash checks at SSI and RCC continued to increase. Galston testified that she did not seek approval from Douglas Radtke to use cash checks on later jobs because she felt that “he’d approved the risk involved ... with doing this.” (T. Tr. at 304). Galston stated that she sought approval from various other SSI employees, including Scott Radtke, for use of cash checks on large jobs after 1998. (Id. at 306).

In 1999, SSI won a contract to erect scaffolding for a government-financed project at the Minneapolis-St. Paul International Airport. The contract for the job called for a certified payroll. The certification would require SSI to attest that proper withholding had been accomplished. Not realizing this until after the job had been completed, SSI paid some workers in cash checks. When faced with a certification requirement that would force her either to report amounts paid with cash checks, revealing that no withholding had taken place with respect to those amounts, or to underreport the hours worked, Gal-ston testified that she chose to exclude some of the hours worked for cash checks.

Testimony was unanimous at trial that cash checks were the subject of a discussion between Galston, Such, and Douglas Radtke occurring after the HERC job, but the nature of the discussion differed in the recollections of various witnesses. According to Galston, the discussion was prompted by Such’s request to use cash checks on a large job. Galston felt obligated to bring to Douglas Radtke’s attention the fact that workers not on the regular payroll of SSI or RCC would not be covered by workers’ compensation insurance if they were paid only in cash checks. She also remembered Douglas Radtke stating “very loudfly]” at one point “no more cash this year.” (T. Tr. at 806).

Douglas Radtke, by contrast, recounted hearing a discussion between Galston and Such regarding the use of cash checks on an upcoming job. Douglas Radtke testified that he “became very angry” and “got right in the middle of the discussion,” telling Such to refrain from using cash checks because' workers paid in this manner would not be covered by workers’ compensation, and any injured worker would “end up suing us.” (T. Tr. at 1542-43).

Scott Such described a conversation in which Douglas Radtke ordered him to “back the cash payroll down to just our main employees” so that he would not “end up in jail.” (T. Tr. at 816). An RCC-employed carpenter testified that Such told him that Douglas Radtke had said the cash payroll was to be discontinued. Do-nohoe also testified to hearing Douglas Radtke yell “no more cash this year,” or “no more cash.”

SSI and RCC ceased their use of cash checks as calendar year 1999 drew to a close. On February 29, 2000, IRS agents executed a search warrant at the companies’ offices, seizing documents and interviewing employees.

A grand jury indicted the appellants, along with Marc Radtke, Rita Galston, and Vernon L. Bodin (a vice-president of SSI), on July 29, 2002, charging each with conspiracy to (1) defraud the United States and the IRS and (2) commit the following offenses: failing to account for or pay over tax, in violation of 26 U.S.C. § 7202, subscribing to materially false tax returns, in violation of 26 U.S.C. § 7206(1), and mail fraud, in violation of 18 U.S.C. § 1341, all in violation of 18 U.S.C. § 371 (together, the “conspiracy count”). The grand jury also indicted the defendants on three counts of mail fraud and three counts of falsifying ERISA records, in violation of 18 U.S.C. §§ 2(b) and 1027. Douglas Radtke and Galston were charged with fifteen counts of failing to account for or pay over tax, in violation of 26 U.S.C. § 7202, and Galston was charged separately with fifteen counts of subscribing to materially false tax returns, in violation of 26 U.S.C. § 7206(1).

Galston pled guilty to the conspiracy count, one count of failing to collect and pay over taxes, and one count of falsifying ERISA records. The appellants, along with Marc Radtke and Vernon L. Bodin, were tried together. The jury convicted Douglas Radtke, Scott Radtke, and Michael Donohoe of the conspiracy count. Douglas Radtke was also found guilty on seven counts of failing to collect, account for, and pay over tax, and on two counts of mail fraud. The jury found Michael Dono-hoe guilty of filing a false and fraudulent tax return and on three counts of mail fraud. Scott Radtke was convicted of three counts of mail fraud. The jury acquitted Marc Radtke and Bodin on all counts.

Douglas Radtke, Scott Radtke, and Do-nohoe were sentenced on April 13, 2004. Douglas Radtke received thirty-six months’ imprisonment, a fine of $20,114.67, and restitution of $179,885.33 — with $132,012.30 going to Wilson McShane, the third-party administrator of the Union’s Fringe Benefit Fund, and $47,873.03 going to Berkley Risk Administrators. Scott Radtke was sentenced to twenty-four months in prison and to joint and several liability for the fine and restitution amounts also owed by his father. Dono-hoe received eighteen months’ imprisonment and joint and several liability with his co-defendants on the fíne and restitution amounts.

II.

On appeal, all three defendants challenge the sufficiency of the evidence to support their convictions. In reviewing a claim of insufficient evidence, we consider the evidence in the light most favorable to the jury’s verdict, and accept as established all reasonable inferences from the evidence that support the verdict. United States v. Hawkey, 148 F.3d 920, 923 (8th Cir.1998). We will reverse only if no reasonable jury could have found the defendant guilty beyond a reasonable doubt. United States v. Walker, 393 F.3d 842, 846 (8th Cir.2005). After carefully considering the record, we find that the evidence presented to the jury was sufficient to sustain its verdict with respect to all three defendants.

A.

Douglas Radtke argues that the evidence presented at trial was insufficient to prove that he acted with the mental state required by the crimes for which he was convicted. He argues that “[e]ach of the offenses charged in the Indictment required proof that [he] acted with intent to defraud.” (D. Radtke Br. at 45). According to Douglas Radtke, the evidence showed only that Galston instigated the use of cash checks, and that he permitted the practice in the good faith belief, formed in reliance on Galston’s advice, that it was legal to pay casual workers as independent contractors. He points to the fact that he signed only four of the nearly 600 cash checks introduced into evidence, and that each of these was to compensate casual Workers.

We believe that sufficient evidence was presented at trial to support the jury’s finding of intent. There was testimony that Douglas Radtke recognized that the practice of using cash checks was illegal, but proceeded to authorize such checks. Galston, Such, and Donohoe, for example, all testified to their recollection of a 1999 meeting at which Douglas Radtke expressed concern about the legal consequences of continuing the use of cash checks. According to Such, he acknowledged that such consequences included jail time. Galston also testified to an April 1998 meeting at which she explained to Douglas Radtke that fines and penalties would result from the use of cash checks on the HERC job if the practice was discovered.

Douglas Radtke asserts that Galston’s testimony regarding the 1998 meeting was not credible because Such did not recall the meeting despite allegedly being present. This argument is unpersuasive. Credibility determinations, of course, are for the jury to make, and even a co-conspirator’s testimony need not be corroborated to be believable. United States v. Anderson, 654 F.2d 1264, 1270 (8th Cir.1981). Douglas Radtke also claims that no reasonable jury could have believed Galston because “evidence at trial was uncontroverted that [Douglas] Radtke was in Annamaria, Florida during the precise time Ms. Galston claims to have met with him and Mr. Such.” (D. Radtke Br. at 47). It is true that Douglas Radtke presented evidence suggesting that he was in Florida during the week of April 21, 1998. The date of the meeting, however, was never placed in that week with certainty — Gal-ston Offered only a “guesstimat[e],” (T. Tr. at 420) — and Douglas Radtke does not claim to have been in Florida for the entire month of April. The jury, in fact, heard evidence that Douglas Radtke was in Minnesota when Scott Such was planning the 1998 HERC job. It would have been reasonable for the jury, therefore, to conclude that Douglas Radtke was present at a meeting at which the illegality of cash checks was discussed.

In any event, intent to defraud need not be proved by direct evidence. E.g., United States v. Ervasti, 201 F.3d 1029, 1087 (8th Cir.2000). The required intent can be inferred from the actions of the defendant. The jury received a considerable volume of circumstantial evidence from which it could have inferred the requisite mens rea. For example, Douglas Radtke was the CEO and President of SSI and RCC, and the jury heard testimony that he was a “hands-on” manager who was involved in the daily operation of the companies. Evidence was presented suggesting that he personally profited by $28,000 as a result of using cash checks at the HERC project in 1999. This evidence gave rise to a sufficiently strong inference of intent to defraud to permit the jury to find that Douglas Radtke committed the charged offenses.

B.

Scott Radtke similarly maintains that the evidence presented at trial established only that he was present at SSI during the time of the alleged conspiracy and that he knew of the illegal use of cash checks. This is insufficient to sustain his convictions, he contends, because the government failed to present “any credible evidence that he was a willing participant in any plan to defraud the [IRS] or... the carpenters union.” (S. Radtke Br. at 22). He also alleges that the government “offered little” to discredit his assertion that he relied in good faith on Galston’s advice regarding the use of cash checks. (Id.).

We disagree. As noted above, intent to defraud can be proven by circumstantial evidence, and Scott Radtke admits that he “was familiar with the use of ‘cash checks’ to pay for casual, extra hours labor.” (Scott Radtke Br. at 13). He also concedes that his signature appears on a cash cheek that was shown to the jury, and that a witness testified to having heard him discuss the use of non-employee names on checks. Galston testified that she obtained approval for the use of cash checks from Scott Radtke, and complained to him regarding Scott Such’s use of such checks. Finally, Galston testified to a meeting she had with Scott Radtke at which they discussed ways to avoid revealing the use of cash checks when they were required to certify a payroll. This evidence of Scott Radtke’s knowledge of and involvement in the cash check scheme provided sufficient support for the jury’s verdict.

C.

Donohoe also argues that there was insufficient evidence to sustain a finding that he was guilty beyond a reasonable doubt of the conspiracy count and of mail fraud. In challenging his conviction for conspiracy, Donohoe maintains that there was insufficient evidence to show that he intended to defraud the IRS, and that his lack of intent to defraud precluded him from joining the alleged conspiracy. Donohoe argues that he relied in good faith on Galston’s assurances that the use of cash checks was legal, and that he was “uneducated as to the workings of the IRS rules and regulations.” (Donohoe Br. at 15). Donohoe’s testimony at trial, however, undermines his protestations of good faith. Donohoe testified that he initially thought the use of the cash checks sounded “fishy.” (T. Tr. at 2290). His wife questioned the legality of the practice when Donohoe told her he needed to use her name for a cash check, and Donohoe recalled Galston instructing him not to use the social security numbers of dead people for cash checks, because doing so would risk detection. The evidence presented at trial, in sum, supported the jury’s determination that Donohoe had the state of mind required to join the fraudulent conspiracy.

Also with respect to his conviction on the conspiracy count, Donohoe argues that while the indictment alleged a conspiracy to defraud both the IRS and “union workers,” (Donohoe Br. at 14), the government failed to prove that the fraud targeted at different victims constituted a single conspiracy rather than two separate conspiracies. Where the evidence at trial supports multiple conspiracies, but only a single conspiracy is charged in the indictment, we reverse only “if the evidence does not support the single conspiracy and the defendant was prejudiced by the variance between the indictment and the proof.” United States v. Pullman, 187 F.3d 816, 821 (8th Cir.1999); see also Kotteakos v. United States, 328 U.S. 750, 756-57, 66 S.Ct. 1239, 90 L.Ed. 1557 (1946).

Whether a given case involves single or multiple conspiracies depends on “whether there was ‘one overall agreement’ to perform various functions to achieve the objectives of the conspiracy.” United States v. Massa, 740 F.2d 629, 636 (8th Cir.1984) (internal quotation omitted). This is determined by the totality of the circumstances, and because it is a question of fact, we draw all reasonable inferences in favor of the verdict. United States v. McCarthy, 97 F.3d 1562, 1571 (8th Cir.1996). Relevant factors “includ[e] the nature of the activities involved, the location where the alleged events of the conspiracy took place, the identity of the conspirators involved, and the time frame in which the acts occurred.” Id. (internal quotation omitted).

Here, the evidence supported a finding that there was a single conspiracy. The conspiracy in which Donohoe allegedly participated involved defrauding the IRS, but the conspiracy count of the indictment did not allege specifically that union workers were also the target of the appellants’ fraudulent scheme. Some of the conduct charged, it is true, was directed at the Union, but a conspiracy with multiple objectives is not the same thing as multiple conspiracies. See Pullman, 187 F.3d at 820-21. Any fraud against the Union depended on a similar mechanism as that against the IRS, namely, the use of cash checks. All of the fraud took place either at the combined headquarters of SSI or RCC, or at company job sites. The identity of the conspirators was equally uniform: Douglas Radtke, Scott Radtke, and Donohoe all were accused and convicted of participating in the same fraudulent conspiracy. And the time frame for all of the allegedly fraudulent conduct was similar. The mailing of fraudulent reports to the Union’s fringe benefit fund third party administrator occurred from November 15, 1997, through November 15, 1999. Most of the cash checks were issued over a similar time period, between April 1998 and December 1999. The evidence thus supports the existence of a single conspiracy-

Donohoe argues further that there was insufficient evidence of his knowledge of the filing of fringe benefit reports to support his mail fraud conviction. This contention is without merit. First, knowledge of the actual instance of mailing the “matter or thing” alleged to have furthered a fraudulent scheme is not an element of the crime described by 18 U.S.C. § 1341. The statute requires only that the defendant devise a “scheme or artifice to defraud” and cause the placement of “any matter or thing” in the mails with the “purpose of executing such scheme or artifice.” Id. The requirement that the defendant cause' the matter or thing to be mailed is satisfied by a showing that he “did an act with the knowledge that the use of mails would follow in the ordinary course of business or that the use of mails reasonably could have been foreseen even though not actually intended.” United States v. Freitag, 768 F.2d 240, 243 (8th Cir.1985). The jury was instructed that it could find Donohoe guilty if the other elements, of mail fraud were shown and “it was reasonably foreseeable that the mail would be used.” (T. Tr. at 2669). Donohoe testified at trial that, during the time he worked for SSI, he “assume[d]” that SSI was meeting reporting requirements by reference to his time card information, and that he was familiar with the Union fringe benefit fund. (T. Tr. at 2243). He also testified that he knew the hours paid for with cash checks would not be reported to the Union. (T. Tr. at 2361). The jury’s conclusion after hearing this testimony that Donohoe “caused” the fringe benefit forms to be mailed for purposes of § 1341 was reasonable.

Donohoe challenges the sufficiency of the government’s showing that he intended to file fraudulent reports to the Union. Donohoe’s testimony and other evidence presented at trial refutes this contention. Donohoe testified that he knew the use of cash checks would result in non-payment of union benefits, yet he admitted that he authorized payment in the form of cash checks some ninety times. The government presented evidence during its cross-examination of Donohoe, moreover, suggesting he used cash checks with the express purpose of avoiding compliance with the Union’s four-hour minimum rate. In short, the evidence of Donohoe’s complicity in short-changing the Union was sufficient to "sustain his conviction for mail fraud.

III.

In a challenge to his conviction for willfully subscribing to a known false tax return, see 26 U.S.C. § 7206, Donohoe asserts that the district court erred in excluding from evidence his amended return for tax year 1999. Donohoe concedes that he did not report $4,330 in income received in the form of cash checks on his original 1999 tax return. His defense at trial was that he did not have to declare the $4,330 'because it was not included in his W-2 form. To bolster this defense, Donohoe sought to introduce evidence regarding an amended tax return on which he reported the $4,330 after realizing it was properly classified as income. The district court granted the government’s motion in limine to exclude evidence of the amended return.

We review a district court’s ex: elusion of evidence for abuse of discretion. United States v. Martin, 369 F.3d 1046, 1058 (8th Cir.2004). “The district court has considerable discretion in admitting evidence of acts of subsequent conduct of a defendant offered to prove the absence of evil intent.” United States v. Woosley, 761 F.2d 445, 449 (8th Cir.1985). “[A]n ever-present reason demanding latitude for [a court’s] ruling on admissibility is that what takes place, particularly after the fact, is often feigned and artificial.” Post v. United States, 407 F.2d 319, 325 (D.C.Cir.1968) (internal quotation omitted). Whether evidence of a defendant’s subsequent mental state, as demonstrated by a subsequent act, is “of any probative value in establishing his state of mind at the time of the alleged criminal acts” must be determined by the circumstances of the individual case. United States v. Stoehr, 196 F.2d 276, 282 (3d Cir.1952).

Donohoe urges us to follow the First, Second, and Seventh Circuits, which, he asserts, “have allowed the introduction of amended tax returns to show good faith.” (Donohoe Br. at 18). He points to three illustrative cases: United States v. Johnson, 893 F.2d 451, 454 (1st Cir.1990); United States v. Dyer, 922 F.2d 105, 108 (2d Cir.1990); and United States v. Tishberg, 854 F.2d 1070, 1073 (7th Cir.1988). None of the cases cited by Donohoe holds that amended tax returns tend to prove a taxpayer’s lack of criminal intent when filing an original return. In Tishberg, for example, the admissibility of the amended return was not considered on appeal — the court stated during a discussion of the sufficiency of the evidence that the defendant’s amended return “may demonstrate a good faith effort to correct his previous mistakes.” Tishberg, 854 F.2d at 1073. The court went on to say that the return “does not, however, negate the import of his previous action.” Id. The suggestion that an amended return may demonstrate good faith in Tishberg does not control Donohoe’s situation because the good faith referred to in Tishberg is a “good faith effort to correct ... previous mistakes,” id., not, as was in question in Donohoe’s trial, good faith at the time the original return was filed. Donohoe’s reliance on Dyer and Johnson is similarly unavailing.

Whether an amended tax return filed post-indictment technically might be “relevant” to the taxpayer’s intent at the time he filed the original return, there is no doubt that self-serving exculpatory acts performed substantially after a defendant’s wrongdoing is discovered are of minimal probative value as to his state of mind at the time of the alleged crime. The district court excluded this evidence because it was of “[of] no probative value, and at best ... confusing to] the jury.” (T. Tr. at 1227). Federal Rule of Evidence 403 provides that evidence, though relevant, “may be excluded if its probative value is substantially outweighed by the danger of ... confusion of the issues, or misleading the jury.” Given that there was little, if any, probative value in Donohoe’s amended filing, see United States v. Ross, 626 F.2d 77, 81 (9th Cir.1980) (holding that the defendant’s filing of subsequent accurate tax returns and his offer to pay any delinquent taxes were not relevant to the charge that he had willfully failed to file tax returns in previous years), the district court did not abuse its discretion in ruling that any minimal probative value was substantially outweighed by danger of confusing the issues and misleading the jury.

IV.

The appellants raise two assertions of error with respect to their sentencings: the district court’s calculation of the amounts of loss for which they were held responsible, and the court’s consideration of facts that were not found by a jury beyond a reasonable doubt. Douglas Radtke also challenges the two-level adjustment he received for his role in the offense pursuant to USSG § 3B1.1.

A.

Appellants each were sentenced based on an identical fraud loss amount, and they challenge several aspects of the district court’s calculation of this amount. We review a sentencing court’s determination of amount of loss for clear error. United States v. Baker, 200 F.3d 558, 561 (8th Cir.2000). In determining the amount of loss attributable to fraud, precision is not required; the sentencing court “need only make a reasonable estimate of the loss.” USSG § 2B1.1, comment. (n.3(C)). Here, the district court computed the fraud loss amount as a total of two elements: union benefit contributions that were not paid as a result of the use of cash checks and the use of SSI as a non-union alter ego for RCC, totaling $132,012.30, and workers’ compensation premiums that were not paid as a result of the use of cash checks, totaling $47,873.03. This resulted in a total loss amount of $179,885.33.

1.

The appellants argue that the district court erred by counting as fraud loss $62,685.13 in Union benefit payments not made by SSI. They contend that SSI’s non-payment was not relevant conduct because SSI was not subject to a collective bargaining agreement with any union, and because SSI’s non-payment was not alleged as criminal activity in their indictment. We disagree.

At trial, the district court heard testimony that SSI payroll employees performed work that was covered by RCC’s collective bargaining agreement, and that SSI was an alter ego of RCC. Its finding that SSI was bound by RCC’s collective bargaining agreement was not clearly erroneous. The fact that SSI’s nonpayment is only obliquely referenced in the indictment, moreover, does not preclude the district court’s consideration of this conduct in determining the amount of loss due to fraud under the guidelines. Relevant conduct under the guidelines need not be charged to be considered in sentencing, and it includes all acts and omissions “that were part of the same course of conduct or common scheme or plan as the offense of conviction.” USSG § lB1.3(a)(2). The district court concluded that SSI’s nonpayment of benefit contributions was “absolutely a portion of the criminal conduct.” (S. Tr. at 109). The court reasoned that RCC and SSI, as alter egos, both benefited at the expense of their employees by accepting their labors while shortchanging them -in health-care coverage, vacation pay, and retirement benefits by not contributing to the Union’s benefit fund. (Id.). The court’s determination that SSI’s nonpayment of benefit contributions was part of the same course of conduct as the use of cash checks was not clear error.

2.

Douglas Radtke argues that the loss 'amount should have been reduced by the amount of benefits SSI paid to its employees. Radtke argues that although RCC and SSI failed to make contributions to Wilson McShane, the third-party administrator of the Union’s Fringe Benefit Fund, which contributions would have entitled employees to various future benefits, the district court should have “credited” against the loss certain amounts that the companies spent to give different benefits to the same employees. Radtke does not specify what amounts should have been credited on this basis. (D. Radtke Br. at 40-41).

The sentencing guidelines provide that in a case involving fraud, loss shall be reduced by “[t]he money returned, and the fair market value of the property returned and the services rendered, by the defendant or other persons acting jointly with the defendant, to the victim before the offense was detected.” USSG § 2B1.1, comment. (n.3(E)(i)). We do not think the fringe benefits paid by SSI or RCC- to employees is the sort of credit against loss contemplated by the guidelines. The commentary to the guidelines provides that the court should apply a credit where the defendant returns the very money or property taken as part of the fraud'. In this case, for example, if Radtke had made arrangements to contribute funds belatedly to the third-party administrator before the fraud was detected, the principle of “credits against loss” likely would apply. But Radtke seeks a credit for other benefits provided to employee-victims that do not correlate directly with the amounts withheld from the third-party administrator as part of the fraud. We find no authority to support this proposition, and we are not of a mind to extend the availability of credits against loss to benefits like these, which were paid to employees as part of a plan to entice them to accept cash checks and thus to further the scheme to defraud. See United States v. Whatley, 133 F.3d 601, 606 (8th Cir.1998) (“[W]e are not inclined to allow the defendants ... a credit for money spent perpetuating a fraud.”); cf. United States v. Carrozzella, 105 F.3d 796, 805 (2d Cir.1997) (explaining that one reason for rule that funds returned as part of investment scheme are not credited against loss is that “the return of money as interest or other income 4s often necessary for the scheme to continue”).

3.

Appellants also charge as error the district court’s • determination that $47,873.03 in workers’ compensation was not paid as a result of their conduct. They argue that the correct amount of loss attributable to non-payment of workers’ compensation premiums was $23,036.63. We do not believe the district court’s finding was clearly erroneous.

Both RCC and SSI paid for workers’ compensation coverage at two rates, a “high rate” and a “low rate,” depending on what type of work was performed by the covered employees. The high rate was paid for more dangerous scaffolding work done at substantial elevations (“high work”), while the low rate was paid for work on the ground or at low elevations. The high rate for the years in question varied between 36.18 percent and 45.19 percent of all wages paid for high work. The low rate ranged from 3.94 percent to 8.66 percent. The district court found that 50 percent of the wages paid in cash checks were for high work, and arrived at $47,873.03 as the workers’ compensation loss.

Appellants contend that the district court erred by finding that 50 percent of the work paid for with cash checks was high work. They allege that “uncontro-verted” testimony established that only 12 percent of work was in the high work category, and that the correct loss figure was therefore $23,036.63. We do not believe this is an accurate characterization of the evidence before the district court.

To be sure, appellants introduced a spreadsheet prepared by the new owner of SSI suggesting that only 12 percent of wages paid in cash checks was for high work. (Defendant’s Ex. S — 5). An audit supervisor from Berkley Risk Administrators, RCC’s third-party administrator for workers’ compensation, also testified that although he did not know “offhand” what percentage of the workers’ compensation premiums were for high versus low work, (S. Tr. at 47), the appellants’ spreadsheet indicated that about 12 percent of RCC’s workers’ compensation premiums were in the high category. (Id. at 57). At trial, however, Galston provided testimony that was sufficient to support an inference that a much higher percentage of cash checks were used for high work. When asked to explain “what the company would save in workers’ compensation from paying cash,” Galston answered that “our base rate on scaffold erection, workers’ comp, was 45 percent of the wages paid, that’s 45 dollars per hundred in wages.” (T. Tr. 294). Although the evidence was not further developed, Galston’s testimony could be understood to mean that most or all of the cash checks were used to compensate workers for high work, because rates for low work never approached the 45 percent rate testified to by Galston. In that sense, therefore, the district court was presented with two divergent possibilities — that only 12 percent of cash checks were used to compensate workers for high work, as suggested by the appellants’ spreadsheet, or that nearly all of the cash checks were so used, as suggested by Galston’s testimony.

If the district court had found that 100 percent of wages paid by RCC and SSI required workers’ compensation payments of 45 percent, the loss attributable to the non-payment of workers’ compensation would have been $77,463.56. The 12 percent figure suggested by defendants would have led to a loss amount of $23,036.63. Instead of choosing either of these figures, the district court settled on 50 percent as an appropriate apportionment, because the defendants’ actions had made “precise calculation virtually impossible,” (S. Tr. at 110), and because the court did not want to “adopt any interpretation which would ... reward the defendants for their deceptive acts.” (Id.). The court observed that “a very substantial portion of the cash payments were made for work on the HERO job,” in which “there was a necessary amount of scaffolding involved,” and in a project at the airport, which also involved considerable scaffolding. (S. Tr. 110).

We cannot say the district court’s finding was clearly erroneous. The district court was required only to make a “reasonable estimate of the loss.” USSG § 2B1.1, comment. (n.3(C)). Where, as here, the loss attributable to fraudulent conduct is unclear because the relevant conduct involved “deceit and secrecy,” moreover, it can be reasonable for a sentencing judge to “split the difference” between two possible extremes. United States v. Berndt, 86 F.3d 803, 811 (8th Cir.1996). The fraudulent conduct here— the use of cash checks — prevented proper record keeping, so the amount of workers’ compensation premiums that went unpaid was not documented. The district court’s determination that 50 percent was the appropriate percentage of work characterized as high work, therefore, was not clear error.

4.

Douglas Radtke asserts that the district court erred by including in the amount of loss all benefits that RCC and SSI failed to pay by use of cash checks prior to April 1998. Because Douglas Radtke was acquitted by the jury of all conduct occurring prior to April 1998, he argues, the district court erred in refusing to “exclude all losses occurring prior to” this date. (D. Radtke Br. at 42). The jury’s acquittal of Douglas Radtke with respect to all pre-April 1998 conduct, however, establishes only that there was reasonable doubt as to his involvement in such conduct. The district court was still free, indeed obliged, to consider whether his involvement had been proved by a preponderance of the evidence. See United States v. Dabney, 367 F.3d 1040, 1043 (8th Cir.2004). The district court properly relied on the evidence at trial of Douglas Radtke’s prior involvement in finding him responsible for the pre-April 1998 loss amounts by a preponderance of the evidence.

5.

Scott Radtke maintains that the loss amount for which he is accountable should not include amounts attributable to SSI, because he was not working for either RCC or SSI when RCC was “revived in the mid-1980s.” Therefore, he argues, he was not part of any illegal “double-breasting” scheme between RCC and SSI. Scott Radtke was part of SSI’s ownership and management, however, and the district court found that SSI and RCC were operating as alter egos during his tenure. Scott Radtke was found guilty of participation in the cash check scheme that involved both companies and therefore his non-involvement in RCC’s revival some twelve years before the scheme began is irrelevant to the loss amount attributable to him.

6.

Donohoe suggests that he should be held responsible only for the loss attributable to the cash checks he personally signed. He maintains that he should not be held responsible for the entire loss attributable to the cash check scheme because he was not involved in starting the scheme, had no decision-making authority at SSI, and was involved in only a small number of cash check payments. (Donohoe Br. at 22). We disagree. Where, as here, criminal activity is jointly undertaken, relevant conduct is to be determined on the basis of all acts and omissions “that were part of the same course of conduct or common scheme or plan as the offense of conviction.” USSG § lB1.3(a)(2). “[T]he amount of loss charged to a particular defendant need not be limited to the money that [the defendant] personally handled. Instead, the amount of loss may include those losses caused by reasonably foreseeable acts that co-workers committed to further the scheme to defraud.” United States v. Whatley, 133 F.3d at 606-07. According to evidence presented at trial, Donohoe was a project manager with SSI who was intimately involved in the cash check scheme, personally authorizing cash checks to employees some ninety times, and receiving payment in cash checks numerous times under eight different names. He also discussed the use of cash checks with Galston and knew that others at the company were involved in the scheme. Under these circumstances, we conclude that the district court’s determination that the entire cash check scheme was reasonably foreseeable by Donohoe is not clearly erroneous.

B.

Douglas Radtke contends that the district court clearly erred in enhancing his sentence two levels on the basis of his role as an organizer and leader pursuant to USSG § 3Bl.l(c). He argues that his mere position as owner of SSI and RCC cannot alone justify this enhancement, and that Rita Galston instigated and expanded the cash check scheme without his knowledge. “[S]ection 3B1.1 focuses on the relative responsibility within a criminal organization.” Ervasti, 201 F.3d at 1041. In determining whether a defendant is an organizer or leader, relevant factors include the defendant’s “exercise of decision making authority, the nature of [his] participation in the commission of the offense, [his] recruitment of accomplices, [his] claimed right to a larger share of the fruits of the crime, the degree of [his] participation in planning or organizing the offense, the nature and scope of the illegal activity, and the degree of control and authority [he] exercised over others.” USSG § 3B1.1, cmt. (n.4).

Douglas Radtke was the CEO and owner of both RCC and SSI. Radtke argues that a business owner does not perform an aggravating role merely because crime is committed on the business premises, or because employees of the company participated in the illegal activity. See United States v. Burgos, 324 F.3d 88, 93 (2d Cir.2003). Douglas Radtke’s role, however, involved more than mere ownership of the business. Testimony at trial supported findings that, in his capacity as CEO and owner, Douglas Radtke expressly authorized his subordinates to use cash checks while knowing of the checks’ illegality and that, by virtue of his position as owner, he received a disproportionate share of the profits derived therefrom. We conclude that the district court did not clearly err in its determination that Douglas Radtke was an organizer and leader in the cash check scheme.

C.

All three appellants have raised the possible applicability to their cases of the Supreme Court’s decision in United States v. Booker, — U.S.-, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005), which was pending when this case was submitted. Booker held that the Sixth Amendment precludes a sentencing judge from imposing a sentence under mandatory sentencing guidelines greater than what could be imposed based solely on facts admitted by the defendant or proved to a jury beyond a reasonable doubt. Id. at 756. As a remedy, the Court declared the sentencing guidelines effectively advisory in all cases. Id. at 765.

The appellants did not challenge the constitutionality or mandatory nature of the guidelines in the district court, so we review their claims under Booker for plain error. See United States v. Pirani, 406 F.3d 543, 550 (8th Cir.2005) (en bane). On review for plain error, we will only reverse if the district court made an obvious error that impinged the substantial rights of the appellants and seriously affected the fairness, integrity, or public reputation of the judicial proceedings. Id.

Although, by applying the guidelines as mandatory, the district court made an “obvious error” for purposes of plain error review, the appellants have not shown that their substantial rights were affected by this error. The record does not establish a reasonable probability that any of the appellants’ sentences would have been more favorable had the district court known that the guidelines were advisory. See id. at 552. Scott Radtke and Michael Donohoe were sentenced at the low end of their respective guideline ranges, but this fact, standing alone, is not sufficient “to demonstrate a reasonable probability that the court would have imposed a lesser sentence” in the absence of mandatory guidelines. Id. at 553. A forti-ori, Douglas Radtke’s sentence in the middle of the guideline range is insufficient to meet the Pirani standard for demonstrating an effect on substantial rights.

The district court gave no indication that it believed the sentences imposed were unreasonable, or that it would have given any of the appellants a lesser sentence in the absence of mandatory guidelines. Although the court acknowledged that “the Court’s discretion is heavily influenced by the sentencing guidelines,” and that “the Court is obligated to ... place ... [its] first determination based on [them],” (S. Tr. at 138), it did not rely solely on the guidelines calculations to justify the sentences it imposed. Instead, the court discussed at length the individual culpability of each of the defendants. (S. Tr. at 123-24, 138-40, 145-47, 158). Where the effect of the error is “uncertain or indeterminate — where we would have to speculate,” a defendant cannot meet his burden to show plain error warranting relief. Pirani, 406 F.3d at 553. Because the record does not establish a reasonable probability that any of the appellants’ sentences would have been more favorable had the district court known that the guidelines were advisory, resentencing is not warranted.

% * * ‡ ‡

For the foregoing reasons, we affirm the judgments of the district court.

LAY, Circuit Judge,

concurring in part and dissenting in part.

I concur with the majority opinion with the exception of Section IV.A.3, wherein the majority holds the district court did not clearly err in calculating the total amount of workers’ compensation payments omitted as a result of the Defendants’ illegal conduct. The district court did not articulate a single reason why it disbelieved defense witness Terry Gul-brandson, who testified that only twelve percent of the workers involved in this scheme were at the “high” scaffold rate. The difference between 12 percent and 50 percent is significant, and so the district court’s unjustified figures cannot be overlooked by claiming that “precise calculation” is “virtually impossible.” Majority opinion, supra, at 843. Precise calculation is not required, but a reasoned fact-finding process is.

The majority attempts to provide a post-hoe rationalization as to how the district court could have arrived upon this fifty-fifty split, but with all due respect, this is just sheer speculation. The majority reasons, “If the district court had found that 100 percent of wages paid by RCC and SSI required workers’ compensation payments of 45 percent,” then the district court’s calculation might have been reasonable. Majority opinion, supra, at 843 (emphasis added). Unfortunately, the district court did not make that finding, and we are not authorized to speculate.

Rita Galston’s testimony also cannot fairly be said to controvert Terry Gul-brandson’s testimony regarding the percentage of workers at the “high” scaffold rate. Galston’s testimony was non-specific, in the sense that it did not identify whether she was referring to the “high” or “low” rate. It is questionable to infer that she was speaking of the “high” rate, since the “45 percent” figure she mentioned did not even comport with evidence showing that the high rate for the years in question ranged from about 35 to 45 percent. In light of these potential conflicts, using Gal-ston’s testimony to buttress the district court’s suspiciously convenient and otherwise unjustified calculation is simply too speculative.

The district court should have explained why it apportioned 50 percent of the workers’ compensation payments to the “high” rate and 50 percent of the payments to the “low” rate. Since it did not, and since the only evidence on point supports a substantially different apportionment, I respectfully dissent. 
      
      . Douglas Radtke's attack on Galston’s testimony regarding the 1998 meeting proceeded along the following lines: The HERC job began the week of April 21, 1998. April 21 was a Tuesday, and Galston testified that she would "guess[]” that the time of the meeting with Douglas Radtke “would have been Tuesday or Wednesday of the week" that the HERC job was to occur. (T. Tr. at 420). Douglas Radtke and his sister testified that on April 21 and 22 he was in Florida with his family on vacation.
     