#### UNITED STATES of America, Plaintiff-Appellee, v. Walter FROST (95-6011; 96-5722); Robert Eugene Turner (95-6005; 96-5725); Richard Thomas Congo (95-6004); Peggy Young Potter (95-6012; 96-5726); Dennis Allen Faulkner (95-6006; 96-5785), Defendants-Appellants.

Nos. 95-6004, 95-6005, 95-6006, 95-6011, 95-6012, 96-5722, 96-5725, 96-5726 and 96-5785.

United States Court of Appeals, Sixth Circuit.

Argued June 9, 1997.

Decided Sept. 12, 1997.

*352Gary Humble (argued and briefed), Office of the U.S. Attorney, Chattanooga, TN, for Appellee.

W. Thomas Dillard (argued and briefed), Wade V. Davies (briefed), Ritchie, Fels, & Dillard, Knoxville, TN for Walter Frost.

Sam D. Elliott (briefed), Charles J. Gearhiser (argued and briefed), Gearhiser, Peters, Lockaby & Tallant, Chattanooga, TN for Robert Eugene Turner.

William P. Burgess, Jr., (briefed), Patrick M. Tuten (argued and briefed), Huntsville, AL for Richard Thomas Congo.

Bobby Lee Cook (briefed), Cook & Palm-our, Summerville, GA, Jake Arbes (argued and briefed), Atlanta, GA for Peggy Y. Potter.

Stuart E. Smith (briefed), Bell, Richardson, Huntsville, AL, and Dennis Allen Faulkner, pro se.

Before: KEITH, KENNEDY, and MOORE, Circuit Judges.

OPINION

KENNEDY, Circuit Judge.

These five criminal defendants raise numerous issues attacking their convictions and sentences for committing mail fraud against the federal government and the University of Tennessee. One defendant also appeals his conviction for knowingly making a false material declaration before a grand jury. For the following reasons, we AFFIRM in part, REVERSE in part, and REMAND for proceedings consistent with this opinion.

I. Introduction

During the time period at issue, defendant Dr. Walter Frost was a full-time professor and Chairman of the Department of Engineering Science and Mechanics at the University of Tennessee Space Institute (“UTSI”) in Tullahoma, Tennessee. UTSI is a graduate school within the Tennessee school system which offers master’s and Ph.D degrees in science and engineering disciplines. Its students are primarily military and other government personnel.

Frost also is the owner and President of FWG Associates, Inc. (“FWG”), a private atmospheric science research firm based in Tullahoma. As it grew, FWG opened another office in Huntsville, Alabama. FWG relies primarily upon contracts with government agencies such as the National Aeronautics and Space Administration (“NASA”) and the United States Department of Defense.

Defendant Dr. Robert Turner, who obtained his Ph.D in 1976 under Frost, was a part-time professor at UTSI. Turner is a former NASA engineer, and his role at UTSI included the recruitment of NASA employees for the school. In 1989, he became a vice-president of FWG and ran the FWG office in Huntsville. Turner also is the uncle of defendants Faulkner’s and Congo’s wives, who are sisters.

Defendants Dr. Richard Congo, Dr. Dennis Faulkner, and Peggy Potter all were students at UTSI between 1987 and 1990, pursuing either a master’s or Ph.D degree. The primary component of the degree was the completion of either a thesis (for a master’s degree) or a dissertation (for a doctoral degree). Frost served as the major professor and advisor for each student; he also selected the professors who would sit on the committee before which each student defended orally his or her thesis or dissertation. Frost and Turner served on the committee for each student defendant.

During his studies at UTSI, Faulkner worked for the Department of the Army. Congo and Potter worked for NASA while at UTSI.

For reasons explained in detail *infra,*a grand jury issued a thirty-one count Superseding Indictment on March 10, 1995 against defendants. Counts One through Sixteen charged defendants with scheming to defraud the United States of money or property, in violation of the Mail Fraud Act, 18 U.S.C. § 1341. Counts Seventeen through Twenty charged a scheme to defraud the University of Tennessee of its intangible right to the honest services of its employees, Frost and Turner. *See*18 U.S.C. §§ 1341, 1346. The indictment charged Frost and Turner as principals under each of these *353counts, and the student defendants as aiders and abettors. *See*18 U.S.C. § 2. The Superseding Indictment did not charge each student with every count: it charged Congo with Counts One through Seven and Nineteen; Potter with Counts Eight through Twelve and Seventeen; and Faulkner with Counts Thirteen through Sixteen and Twenty. It also charged Charles Hill, a NASA employee who similarly pursued a doctoral degree at UTSI, of Counts Eight through Twelve and Eighteen. Hill, however, died before trial.

Counts Twenty-One through Twenty-Nine charged a scheme to defraud the federal government, in violation of the mail fraud statute, through the submission of false billing claims. Counts Twenty-One and Twenty-Two applied only to Frost and Turner; Counts Twenty-Three through Twenty-Nine applied only to Frost.

Count Thirty charged Frost with attempted obstruction of justice during the investigation resulting in these prosecutions, in violation of 18 U.S.C. § 1503. Finally, Count Thirty-One charged Congo with making a false material declaration to the grand jury during these proceedings, in violation of 18 U.S.C. § 1623.

After unsuccessfully moving to dismiss the indictment, defendants were tried before a jury beginning on March 28,1995. On April 28,1995, the jury convicted each defendant of each count with which he or she had been charged, except that it acquitted Frost and Turner of Count Eighteen, and acquitted Frost of Count Thirty, the obstruction of justice count.

Defendants filed motions for acquittals and new trials, which the District Court denied. Defendants thereafter filed these appeals, and we turn now to the arguments which they have raised.

II. Claims Regarding Mail Fraud Act

A. Scheme to Defraud Federal Government of Contracts

The main theory of the prosecution is that the professor defendants provided each student defendant with written materials and help from FWG employees so that the student could complete his or her thesis or dissertation, and therefore receive an advanced degree, through significant plagiarism and with a minimum of effort. In return for this benefit, the student defendant would abuse his or her position with the government in order to secure for FWG, and through it the professor defendants, lucrative government research contracts, or modifications of contracts. By pursuing this scheme, the professor defendants obtained property from the federal government which they otherwise would not have received, and the student defendants obtained advanced degrees from the University of Tennessee without having done the necessary work.

The government argues that defendants repeatedly violated 18 U.S.C. § 1341, the mail fraud statute, by pursuing this “degrees-for-contraets” scheme. Section 1341 provides:

> Whoever, having devised or intending to devise any scheme or artifice to defraud, or for obtaining money or property by means of false or fraudulent pretenses, representations, or promises, ... for the purpose of executing such scheme or artifice or attempting to do so, places in any post office or authorized depository for mail matter, any matter or thing whatever to be sent or delivered by the Postal Service, ... or takes or receives therefrom, any such matter or thing, or knowingly causes to be delivered by mail or such carrier according to the direction thereon, or at the place at which it is directed to be delivered by the person to whom it is addressed, any such matter or thing, shall be fined under this title or imprisoned not more than five years, or both.

18 U.S.C. § 1341.

Counts Two through Seven, Nine through Twelve, Thirteen, Fourteen, and Sixteen in the Superseding Indictment rested on the degrees-for-contraets scheme. Although the indictment charged Frost and Turner with all of these counts, it charged Congo only with Counts Two through Seven, Potter with Counts Nine through Twelve, and Faulkner with Counts Thirteen, Fourteen, and Sixteen.

*354Ultimately, the prosecution relies upon the following general evidentiary theory. In 1985, Dan Berlinrut, an engineer for the Air Force and a Ph.D candidate under Frost from 1983 to 1986, discussed with Frost his proposed dissertation topic. Frost, copying verbatim large portions of Berlinrut’s dissertation, turned the topic into a proposal for a contract with the Air Force. The Air Force rejected the proposal. Frost thereafter instructed Berlinrut to call Turner, who told Berlinrut that he should award FWG a contract on his dissertation topic when he got to his next duty station. Turner also told Berlinrut that “Frost would then write [his] dissertation guaranteeing it would be accepted,” and that “this was done all the time at NASA, and it is OK.” Rather than accepting this invitation, Berlinrut instead reported this incident to the authorities. He eventually failed to graduate.

The government contends that, several years later, the student defendants, who were both students at UTSI and government employees, cheated with the help of Frost and Turner on their thesis or dissertation. Further, each student defendant had an alleged role in the award or modification of a government contract to FWG. Accordingly, the government argues, we may infer that defendants entered into the same kind of agreement which Turner unsuccessfully proposed to Berlinrut, acting with the intent to defraud the government of its property.

Every defendant attacks the sufficiency of the evidence supporting these convictions. When determining whether sufficient evidence supports a conviction, we decide “whether, after viewing the evidence in the light most favorable to the prosecution, any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.” *United States v. Ellerbee,*73 F.3d 105, 107 (6th Cir.1996)(quoting *Jackson v. Virginia,*443 U.S. 307, 318-19, 99 S.Ct. 2781, 2788-89, 61 L.Ed.2d 560 (1979)). Further, “circumstantial evidence alone can sustain a guilty verdict,” *id.*at n. 2 (quoting *United States v. Stone,*748 F.2d 361, 362 (6th Cir.1984)), and we will draw all reasonable inferences in favor of the prosecution. *See, e.g., United States v. Oldfield,*859 F.2d 392, 399 (6th Cir.1988).

A conviction for mail fraud requires proof of the following three elements:

> (1) devising or intending to devise a scheme to defraud (or to perform specified fraudulent acts);

> (2) involving a use of the mails; and

> (3) for the purpose of executing the scheme or attempting to do so.

*Id.*at 400. A defendant does not commit mail fraud unless he possesses the specific intent to deceive or defraud, *see, e.g., United States v. Smith,*39 F.3d 119, 121-22 (6th Cir.1994); “a scheme to defraud must involve ‘[i]ntentional fraud, consisting in deception intentionally practiced to induce another to part with property or to surrender some legal right, and which accomplishes the end designed.’ ” *American Eagle Credit Corp. v. Gaskins,*920 F.2d 352, 353 (6th Cir.1990)(quoting *Bender v. Southland Corp.,*749 F.2d 1205, 1216 (6th Cir.1984)(quoting *Epstein v. United States,*174 F.2d 754, 765 (6th Cir.1949)))(emphasis deleted).

A defendant may commit mail fraud even if he personally has not used the mails. *See United States v. Griffith,*17 F.3d 865, 874 (6th Cir.1994). A mail fraud conviction requires only a showing that the defendant acted with knowledge that use of the mails would follow in the ordinary course of business, or that a reasonable person would have foreseen use of the mails. *See Oldfield,*859 F.2d at 400. Accordingly, the government. does not have to- show that the defendant actually intended to cause the mails to be used. *See id.*Further, “[t]he mailings may be innocent or even legally necessary.” *Id.*(quoting *United States v. DeCastris,*798 F.2d 261, 263 (7th Cir.1986)). “In sum, the ‘mailing need only be closely related to the scheme and reasonably foreseeable as a result of the defendant’s actions.’” *Id.*(quoting *United States v. Silvano,*812 F.2d 754, 760 (1st Cir.1987)).

We agree with defendants that there is insufficient evidence to uphold the counts that rest upon an alleged scheme to defraud the federal government of property in the form of contract awards. These convictions *355therefore differ from other mail fraud convictions in this case which, although also relating to allegations of academic impropriety, instead charge that defendants defrauded either the University of Tennessee of the honest services of its employees Frost and Turner, or the federal government of tuition money provided to the student defendants. Further, these convictions do not rest upon an allegation that defendants deprived either the public of its intangible right to the honest services of its public servants, or the government of its intangible right to the. honest services of its employees. *See infra*Section II.C (discussing 18 U.S.C. § 1346). Although each defendant happened to be a state or federal government employee, these convictions depend upon a showing that defendants intended to defraud the government, as a business entity, of a property right.

1. Faulkner

In 1986, Faulkner began to work as a civilian electronics engineer at CROSSBOW, an office within the Department of the Army and located at Redstone Arsenal, Alabama. His responsibilities included acting as a Contracting Officer’s Technical Representative (“COTR”) for various government contracts. As a COTR, Faulkner helped to identify the need for contractor assistance, select a qualified contractor, review estimates, monitor performance quality and timeliness, and review progress in relation to expenditures. As a COTR with the Army, he did not control contract money.

Faulkner enrolled in UTSI in the spring of 1987 and selected Frost as his major professor. In the middle of 1987, he began the process of writing a dissertation of the topic of “False Targeting Effects of Turbulent Eddies in Millimeter Frequencies.” After almost two years of effort, Faulkner completed an initial draft of the dissertation. In August or September of 1989, however, he discovered that his dissertation was relying upon classified data. After consultations with Frost and a government official, Faulkner later learned that, because the University of Tennessee had a policy prohibiting classified projects for advanced degrees, he had to select a new topic and begin working on another dissertation.

On November 30, 1987, Joe Durham, the immediate supervisor of Faulkner at CROSSBOW, responded to a proposal from FWG by issuing a letter indicating that CROSSBOW intended to “contract with FWG to analyze classified threat simulator radar systems.” This proposed contract eventually would become the Miscellaneous Defense Activities (“MDA”) contract. Although Faulkner did not select FWG for the contract or participate in the negotiations process, he did prepare sometime in 1988 a memorandum which justified the granting of a sole-source, as opposed to a bid or competitive, contract to FWG. Within the memorandum, Faulkner referred to an informal market survey which he had conducted earlier that year. Faulkner stated in the memorandum that defense contractors other than FWG were unsuitable to perform the MDA contract because they would not sign a hardware waiver. It is undisputed that formal or written market surveys were not required for government contracts worth under a million dollars, such as the MDA contract. Further, Durham testified that competitive defense contracts may pose security risks because they involve the exposure of classified information, and that CROSSBOW did not maintain a single competitive contract during his tenure as a supervisor from 1985 to 1993.

On January 31, 1989, CROSSBOW issued a sole-source letter contract providing that FWG would perform the MDA contract from the date of the letter until July, 1990 in return for $937,248. Faulkner acted as the COTR for the MDA contract during this time.

In the fall of 1989, and shortly after Faulkner learned that he could not complete his first dissertation topic, Frost gave Faulkner three unpublished reports completed by FWG in the mid-1980s and instructed him to produce a new dissertation by combining them. Faulkner completed a rough draft of his new dissertation in early 1990, and a final draft in mid-March of 1990. Faulkner sent copies of the final draft to Frost and the other four members of the academic *356committee before which Faulkner would defend his dissertation. During his oral defense in late March of 1990, Faulkner told the committee that his topic was substantially related to his previous topic and was based upon three FWG studies in which Frost had participated. After Faulkner made the changes suggested by committee members, the committee approved his dissertation and he graduated with a doctor in philosophy degree.

The government introduced evidence that at least ninety-two percent of Faulkner’s second dissertation was plagiarized from the three FWG reports given to him by Frost, and from a conference paper presented by Frost. Although many pages, including the conclusion, represented verbatim excerpts from the FWG reports, they did not contain quotation marks or any citations to the reports.

Frost gave the dissertation to his secretary at FWG, Martha Craddock, to type. Craddock, who spent about three months working occasionally on the project, testified that “part of [typing the dissertation] was cut and paste and pages from other documents that were cut and rearranged and reworded,” and that she recognized some of the dissertation as reports she previously had typed.

As noted, the prosecution alleges that Faulkner committed mail fraud by participating in a scheme to defraud the government by helping to procure the MDA contract for FWG in return for a “free” dissertation. The mailings upon which the degree-for-contract convictions of Faulkner are based are vouchers for the MDA contract mailed from FWG to the government on January 15, February 12, and March 15, 1990. The prosecution cites the testimony of David Baker, an Army policeman, who stated that Faulkner told him during the investigation of these matters that Faulkner never had contacted any companies when conducting his market survey in 1988, but instead had concluded on the basis of his personal knowledge of the industry that contractors other than FWG would be unwilling to sign a hardware waiver. Baker therefore concluded that the 1988 memorandum compiled by Faulkner was false, because “when you say a company will not sign [a waiver], that means that you have ... talked to somebody that can speak for that company. You can’t just, you know, make that decision for the company.” Contrary to the opinion of Baker, however, significant evidence indicates that CROSSBOW frequently did not contact other companies directly when conducting informal market surveys for contracts worth less than one million dollars if the contracts involved classified material.

Regardless of whether it was improper not to contact other companies directly, or whether Faulkner falsely suggested that he had done otherwise, these convictions lack an evidentiary basis simply because Faulkner performed and memorialized the market survey in 1988. From 1987 until 1989, however, he was working on his first dissertation, and there is no dispute that he was the only person to work on that dissertation, or that the scheme to concoct a second plagiarized dissertation did not arise until the fall of 1989. The record therefore fails to contain sufficient proof that Faulkner, with the intent to defraud the government, performed and relied upon an improper market survey in order to reward Frost and Turner for bestowing an illegitimate dissertation.

The prosecution presents an alternative argument. The MDA contract was extended twice: it received an initial extension from July, 1990 to September, 1990, and then again was extended until September, 1991. These extensions raised the total value of the contract to $1,896,501.29. The prosecution asserts that documents entitled “program identification documents” submitted by CROSSBOW employees on March 16 and April 3, 1990 led to these extensions. The prosecution attempts to link Faulkner with the first of these documents, arguing that “even as Faulkner was cutting and pasting Frost’s reports together for his dissertation, he was recommending in March 1990 that FWG get an extension on the contract.”1

*357Although the evidence does indicate that Faulkner was passing off a plagiarized dissertation with the help of Frost in March, 1990, it does not suggest that Faulkner was responsible for extending the MDA contract. Lawrence Duncan, who works for a support organization for the Department of Defense and who served as a contracting officer for the MDA contract until mid-1990, testified for the prosecution. His direct testimony established only that “somebody” asked to extend the MDA contract in March, 1990, and that Faulkner was the COTR for the MDA contract at that time. The prosecution argues that this testimony during redirect examination shows that Faulkner “instigated” the extension:

> Q. Okay. But when that extension was requested in March of 1990, the COTR at that time getting the ball rolling to get that extension started was Dennis Faulkner, wasn’t it?

> A. Yes, sir.

Examination of this exchange and the testimony preceding it reveals that Duncan reaffirmed that Faulkner was the COTR for the MDA contract when an extension was requested. The only material in the record suggesting that Faulkner “got the ball rolling” on the extension was the question posed by the prosecution. The fact that the prosecution attempts to rely solely upon “evidence” created through the phrasing of its own question is highlighted by the fact that Duncan testified during cross-examination that three specific individuals other than Faulkner prepared and signed the March, 1990 program identification document. Duncan further testified that another COTR, Ken McCormick, performed the technical evaluation for the proposed extension, and that the contracting officer who replaced Duncan on the MDA contract, Michael Corbis, “proceeded to do the work on the major contract extension, which was issued by him on the 28th of September of 1990.” The record does not support the assertion that the status of Faulkner as a COTR, standing alone, allows for the inference that he recommended an extension.

Because the record provides insufficient evidence for Faulkner’s convictions for Counts Thirteen, Fourteen, and Sixteen, we do not address the claim by Faulkner that we must reverse these convictions because the prosecution failed to disclose that a government officer who oversaw the MDA contract informed the prosecution that Faulkner had no role in extending the contract. *See infra*Section IV.A, discussing *Brady*claim raised by Frost. Because the prosecution’s case against Frost and Turner on these counts is based solely upon the acts of Faulkner, there is insufficient evidence to support their convictions of Counts Thirteen, Fourteen, and Sixteen.

2. Potter

Potter worked at the Marshall Space Flight Center (“MSFC”) of NASA in Huntsville, Alabama for more than twenty-five years. In 1987, she became a manager in the MSFC Small Business Innovative Research (“SBIR”) program, which sought to identify opportunities in NASA in which small companies and minority firms could participate. Although her bachelor’s degree was in business management, she entered a master’s degree program at UTSI in engineering science under Frost in 1988.

After Potter had informed Frost that she was having difficulty deciding upon a topic for her thesis, he had Turner deliver to Potter a FWG report on a cancelled project concerning a tower and wind study. Either Frost or Turner then gave a diskette containing a copy of the report to Craddock, Frost’s secretary at FWG, who then spent about two days retyping it into a more presentable format. Evidence at trial indicated that Potter’s thesis and the tower and wind study report were ninety-five percent identical.

Before orally defending her thesis before a committee, Potter studied the document which she was submitting in order to be able to express a degree of understanding during her defense. The committee consisted of Frost, Turner, and a Dr. Kenneth Kimble. Although Potter told the committee that she *358had used material from a report given to her, she presented the thesis as her own work. After the University approved her thesis, Potter graduated in December, 1989. Although Potter admitted at trial that she neither wrote her thesis nor did any research, she claimed that Frost had led her to believe that she could satisfy her degree requirements merely by studying, checking, and finalizing the report.

In early 1990, Potter retained control over about $55,000 of an original grant of $110,000 in government funds for an SBIR workshop project. Potter claims that she had difficulty finding individuals or firms willing to perform any workshops for only $55,000, and that, under NASA rules, any funds which had not been committed by September, 1990 would expire and no longer be available to NASA. Accordingly, Potter asserts that she was interested when Frost approached her after she had graduated and informed her that FWG was interested in submitting a proposal to perform such workshops for as little as $50,000. Due to procedural difficulties with obtaining or accessing government funds, however, Potter decided to accept a suggestion made by either Frost or Turner: merely attempt to transfer the $55,000 in remaining funds to the “winds measurement” contract, an existing contract between FWG and NASA, in order to avoid the unwanted process of lengthy negotiations over a new contract, as well as termination of the funds before approval of the workshop proposal submitted by FWG. Kelly Hill, who had been a defendant in these prosecutions but who died before trial, was the COTR for the winds measurement contract.

On April 18, 1990, Potter submitted a procurement request designed to transfer the $55,000 in SBIR funds to the winds measurement contract. On May 9,1990, Hill submitted a technical evaluation which approved of the proposed addition of funds. The evaluation indicated that the funds were targeted for workshops, and that the initial date of the procurement process had been January 2, 1990. Potter’s superiors in the SBIR program never approved the proposal by FWG to perform the workshops, and the added $55,000 was withdrawn from the winds measurement contract.

The prosecution alleges that Potter committed mail fraud by helping to increase the value of the winds measurement contract by $55,000 in return for her thesis. The prosecution apparently claims that the effort to transfer the funds was a fraudulent scheme because the documentation submitted by Hill in May, 1990 deceptively implied that the additional funding was related specifically to the research being performed under the contract (which would have been a proper contract modification), rather than to a business program (which was an improper modification).

The mailings upon which these convictions are based are vouchers for the winds measurement contract mailed from FWG to the government on January 15, February 13, March 15, and April 12, 1990 for work done on the original contract. Potter claims that these vouchers cannot support her convictions because they were unrelated to, and therefore did not further, the fraudulent scheme charged. Even assuming that the jury could infer that Potter intended to defraud the government on the basis of the documentation submitted by Hill, we agree with her that these vouchers were unrelated to the scheme at issue.

The prosecution argues that the vouchers may support the convictions of Potter because 1) the object of the scheme at issue was to enrich Frost and Turner through government contract money; 2) money received as a result of the vouchers at issue did enrich Frost and Turner; 3) therefore, these vouchers furthered the scheme. ■ This argument, however, cannot withstand scrutiny.

“The federal mail fraud statute does not purport to reach all frauds, but only those limited instances in Which the use of the mails is a part of the execution of the fraud----” *United States v. Altman,*48 F.3d 96, 102 (2d Cir.1995)(quoting *Kann v. United States,*323 U.S. 88, 95, 65 S.Ct. 148, 151, 89 L.Ed. 88 (1944)). The mails therefore must serve the purpose of executing or furthering the accomplishment of the scheme. *See United States v. Koen,*982 F.2d 1101, 1107 (7th Cir.1992); *see also Unit**359*ed States v. Downs,*870 F.2d 613, 615 (11th Cir.1989)(completion of scheme must depend in some way upon mailing); *United States v. Wellman,*830 F.2d 1453, 1461 n. 11 (7th Cir.1987)(success of scheme must be linked causally to mailings). Although the use of the mails does not have to be an essential part of the scheme, it does have to be incident to an essential part of the scheme. *See Altman,*48 F.3d at 102; *see also Oldfield,*859 F.2d at 400 (mailing must be “closely related to the scheme”).

In this case, the vouchers relied upon by the prosecution charged only for work performed by FWG up until March, 1990 on the unmodified winds measurement contract. The jury, however, did not convict Potter of fraudulently procuring the unmodified winds measurement contract; Potter had no role in procuring the original winds measurement contract. Regardless of whether Hill or Potter initiated the attempted modification of the contract in January or April, 1990, the vouchers have no relationship to the $55,000 associated with the SBIR program or to the modification, and therefore no relationship to the specific scheme of which Potter was convicted. Although the prosecution argues that because defendants “selected [the winds measurement] contract as the vehicle to get Frost the $55,000, mailings furthering this contract were necessary to the scheme,” the winds measurement contract would continue to exist, and therefore remain a viable vehicle for future fraud, regardless of whether FWG had sent the vouchers. Although the vouchers did allow FWG to receive payments for work already done under the original contract, the payments had nothing to do with extending the contract. They simply did not advance the accomplishment of any scheme to increase the value of the contract. Accordingly, there is insufficient evidence for the convictions of Potter of Counts Nine through Twelve. Because Frost’s and Turner’s convictions of these counts depend upon the same mailings, they also must be vacated.

3. Congo

In the spring of 1987, Turner convinced Congo, a NASA chemist and Ph.D student, to transfer from Auburn to UTSI. During his diagnostic exam, at which UTSI faculty assessed his competency for the doctoral program, Congo explained that his work at NASA involved the assessment of risks posed by incompatible chemicals on the space station project of NASA. That summer, Frost requested Congo to review an informal research project proposal regarding a computer modeling program designed to assess the hazards posed by incompatible chemicals on the space station project of NASA. Shortly thereafter, Frost, on behalf of FWG, submitted to Congo a formal unsolicited proposal for such a research project with NASA. In November of 1987, Congo initiated the procurement process for the proposed project, documented the justification for awarding FWG a sole-source contract, and submitted a favorable technical evaluation summary of the proposal. On March 10, 1988, Congo submitted a formal procurement request for the project, and submitted a procurement request for additional funding on June 23, 1988. By August, 1988, NASA had approved the proposal and awarded FWG a $300,000 contract, for which Congo served as the COTR.

Congo claims that he began to work on his dissertation in August, 1988. Frost was his major professor. The topic of his dissertation was extremely similar to the topic of the chemical hazards contract between NASA and FWG. The government introduced evidence that Turner told Karen Seiser, an FWG employee, to help Congo with his dissertation. Seiser testified that she spent over two eighty-hour weeks in February, 1990 writing about two-thirds of the dissertation, and that Congo treated her like an employee. After she worked on the dissertation, Seiser prepared a report for FWG on the progress of the chemical hazards contract, using many of the sections which she had written for the dissertation. Congo admitted that, as COTR for the contract, he rejected the report because it looked too much like his dissertation. Two other FWG employees also worked on the dissertation, one of whom implemented changes during a period of several days at the direction of Congo.

*360Congo submitted his dissertation on February 26, 1990. Frost, Turner, and three other professors sat on the committee before which Congo orally defended his dissertation. Neither Congo nor Frost nor Turner disclosed the work done by Seiser on the paper. The committee approved the dissertation and Congo graduated.

The prosecution argues that Congo committed mail fraud by participating in a scheme to defraud the government by helping to procure the chemical hazards contract for FWG in return for his dissertation. The mailings upon which the degree-for-contraet convictions of Congo are based are vouchers for the chemical hazards contract mailed from FWG to NASA on April 2, May 8, June 11, July 11, August 10, and September 11, 1990.

Viewing the evidence in the light most favorable to the prosecution, the similarities between the circumstances of Congo and Berlinrut, the student whom Turner unsuccessfully requested to provide a contract in exchange for a dissertation, would allow a rational jury to find that Frost, Turner, and Congo agreed in 1987 that Congo would help procure a contract for FWG in exchange for Frost and Turner eventually providing him with a dissertation. Like Berlinrut, Congo informed Frost and Turner of his specific area of interest. As with Berlinrut, Frost and Turner sought to submit through the student a contract proposal on that very topic to the government agency for which the student worked. Congo also took the same action requested of Berlinrut: helping to provide FWG with a contract involving the topic of his future dissertation. Finally, just as they had offered to do for Berlinrut, Frost and Turner took the very unusual step of having much of Congo’s dissertation written for him. Although there is no direct evidence that Frost and Turner propositioned Congo as they had Berlinrut, the jury still could have inferred from these facts that defendants entered into an arrangement similar to that which Berlinrut had refused.

Nonetheless, the evidence cannot support the convictions for Counts Two through Seven. A mail fraud conviction must rest upon proof of some fraudulent scheme or act. The only deception with which Congo is charged in relation to the government, however, is a failure to disclose his relationship with FWG to his superiors and colleagues at NASA.2 The circumstances relating to Congo therefore differ from those of Potter and Faulkner because the record does not suggest that he committed any deception when helping to secure the chemical hazards contract, other than not disclosing a conflict of interest. Although Congo deceived the University by submitting a dissertation written primarily by other people, the prosecution cannot rely upon this deception in order to convict Congo of a scheme to defraud *the government*of property. We note that the federal circuits are split as to whether a defendant may be convicted of mail fraud for deceiving only persons other than the intended victims of a scheme. *Compare United States v. Blumeyer,*114 F.3d 758, 767-68 (8th Cir.1997)(noting split and following *United States v. Cosentino,*869 F.2d 301, 307 (7th Cir.1989), to hold that defendant commits mail fraud by deceiving regulatory agency in order to forestall regulatory action which would impede scheme to obtain property from others) *with United States v. Sawyer,*85 F.3d 713, 734 n. 18 (1st Cir.1996)(intended victims of scheme must be the ones defrauded); *McEvoy Travel Bureau, Inc. v. Heritage Travel, Inc.,*904 F.2d 786, 794 (1st Cir.1990)(scheme to defraud cannot rest upon deception of one party which causes deprivation to another); *United States v. Utz,*886 F.2d 1148, 1151 (9th Cir.1989)(defendant must intend to obtain money or property from victim of deceit). We do not have to resolve this split, however, because even the cases which have held that convictions may rest upon the deceit of a person other than the ultimate victim contemplated that the deception was causally related to the scheme to obtain property from the victim. *See Blumeyer,*114 F.3d at 767-68; *Cosentino,*869 F.2d at *361307. In this ease, the fact that the benefit received by Congo from Frost and Turner involved academic deception is a fortuity. The acts of plagiarism were irrelevant to the success of the scheme to obtain a government contract; whether Congo received from FWG a bogus dissertation or something as mundane as money did not affect, and was not intended to affect, his ability to help FWG obtain the chemical hazards contract.

Accordingly, the convictions can rest only upon a failure by Congo to disclose his eon'fliet of interest. Many opinions repeat the maxim that “a breach of fiduciary duty alone, without the ‘something more’ of fraudulent intent, cannot constitute mail fraud.” *E.g., Morda v. Klein,*865 F.2d 782, 785 (6th Cir.1989). In *United States v. Mittelstaedt,*31 F.3d 1208 (2d Cir.1994), the Second Circuit helped to define what this “something more” is. Rejecting the claim of the prosecution that the defendant had violated § 1341 merely because his failure to disclose a conflict of interest had prevented the victim from making a fully informed economic decision,3 the *Mittelstaedt*court explained:

> Where an individual standing in a fiduciary relation to another conceals material information that the fiduciary is legally obliged to disclose, that non-disclosure does not give rise to mail fraud liability unless the omission can or does result in some tangible harm. However, lack of information that might have an impact on the decision regarding where [the victim’s] money is spent, without more, is not a tangible harm and therefore does not constitute a deprivation of section 1341 “property.”

> To be material, the information withheld either must be of some independent value or must bear on the ultimate value of the transaction. To convict, the government had to establish that the omission caused (or was intended to cause) actual harm to the [victim] of a pecuniary nature or that the [victim] could have negotiated a better deal for itself if it had not been deceived.

*Id.*at 1217 (citations and emphasis omitted); *see also Emery v. American Gen. Fin., Inc.,*71 F.3d 1343, 1348 (7th Cir.1995)(fiduciary commits mail fraud through misleading omission intended to induce action to disadvantage of misled); *United States v. Starr,*816 F.2d 94, 98 (2d Cir.1987)(deceit must be accompanied by contemplation of harm to victim which affects very nature of alleged bargain between defendant and victim). The *Mittelstaedt*court further indicated that proof that a victim, *acting solely on the basis of general principles,*would have refused to contract if the defendant had disclosed his conflict does not demonstrate a mail fraud violation under § 1341. *See Mittelstaedt,*31 F.3d at 1218. We agree with this analysis and note that it accords with old precedent existing in this circuit. *See Epstein v. United States,*174 F.2d 754 (6th Cir.1949). The *Epstein*court, although recognizing that actual loss to the victim is unnecessary, held that fiduciaries who had not disclosed a conflict of interest did not have the intent to defraud when the evidence showed only that the contracts induced by the defendants were entirely beneficial and fair to the entity denied the disclosures. *See id.*at 764-69.

In order for the jury to convict Congo, the evidence at trial therefore must have permitted a reasonable jury to conclude that Congo intended to inflict a tangible injury upon NASA. We hold that it did not. The sole witness relied upon by the prosecution, Salvadore Caruso, the direct supervisor of Congo at NASA, testified that FWG performed necessary and needed work under the chemical hazards contract, and that NASA was very concerned about the issue of incompatible materials on the space station project. Caruso also testified that he had no reason to believe that FWG had not performed the terms of the contract, or that there had been any complaints regarding the ability of FWG to fulfill the project requirements. There is no evidence in this case that NASA would have had to pay less money or would have received more services if Congo had disclosed his conflict of interest. *Cf. United States v. Dandy,*998 F.2d 1344, 1358 (6th Cir.l993)(upholding mail fraud conviction because, although defendant did not commit *362mail fraud simply by profiting from breach of fiduciary duty to victim, evidence showed that victim had to pay higher prices for goods received under contract because provider of goods was paying kickbacks to defendant). Finally, Caruso testified that nothing about the documentation submitted by Congo was misleading. The record contains no evidence to the contrary of the above.

We therefore hold that, even though the evidence allows a finding that Congo agreed to trade a contract for a dissertation, there was insufficient evidence that he intended to defraud NASA by not disclosing his conflict of interest. Although Congo intended the government to transfer money to FWG, there is no evidence that he intended that the government would not receive in return a necessary service, performed adequately and for a fair price. Because the evidence showed that FWG, and therefore Frost and Turner, fairly and adequately performed a necessary contract not secured through any misrepresentations, we likewise vacate the convictions of Frost and Turner of Counts Two through Seven.

The holding in *United States v. Fischl,*797 F.2d 306 (6th Cir.1986), does not compel a different result. The defendant in *Fischl,*who contracted with the State of Michigan to procure a tug boat, received a kickback from the manufacturer of the engine of the boat. *See id.*at 308. Although the kickback did not injure the State monetarily because the defendant was performing the contract for a fixed price, the State would have cancelled the contract if it had known about the scheme. *See id.*at 309-11. Further, the defendant submitted deceptive accounting documents to the State and lied when a State senator asked him about a possible kickback scheme, which, if true, would have jeopardized continued funding of the tug boat project by the State. *See id.*

The *Fischl*court rejected the claim of the defendant that he had not committed mail fraud because the lack of an injury to the victim revealed that he never had intended to harm the State. *See id.*at 311. Unlike this case, however, the evidence in *Fischl*was not that the defendant merely had failed to disclose a conflict of interest, but that he had made several false statements to further his scheme. *See id.*Further, the *Fischl*court often invoked the intangible rights of the public when justifying its holding. *See id.*at 311-12; *see also United States v. Murphy,*836 F.2d 248, 252-53 (6th Cir.1988)(distinguishing *Fischl*by describing the right of the State of Michigan to complete information as an intangible right). As previously explained, however, the convictions now at issue rest upon the specific claim that defendants intended to deprive the government, acting as a business, of its property.

B. Scheme to Defraud Federal Government of Tuition

The government helped to pay for the advanced degrees of its employees, the student defendants, by paying to UTSI their fees. No student, however, wrote his or her own thesis or dissertation, the primary component of the advanced degree program. Counts One, Eight, and Fifteen in the Superseding Indictment therefore charge defendants with violating § 1341 by defrauding the government of the tuition money. Count One rests upon a September 20, 1989 invoice from UTSI to NASA for the fees of Congo; Count Eight rests upon a July 21, 1989 invoice from UTSI to NASA for the fees of Potter; and Count Fifteen rests upon a February 15, 1990 invoice from UTSI to the Department of the Army for the fees of Faulkner. The indictment charged Frost and Turner with all of these counts, and each student with the count relating to his or her own fees. The jury convicted each defendant of each charged count.

The student defendants urge that the invoices cannot support their convictions because they did not cause or intend the mailings to be sent. This claim is without merit. As explained, a mailing may support a mail fraud conviction as long as the defendant knew that use of the mails would follow in the ordinary course of business, or that a reasonable person would have foreseen use of the mails. *See, e.g., Oldfield,*859 F.2d at 400. A reasonable jury certainly could have found that defendants reasonably should have foreseen that use of the mails would occur when UTSI obtained their tuition mon*363ey from the government. Although defendants also claim that the vouchers did not further execution of the scheme, the success of the scheme to obtain the tuition money obviously was causally linked to, if not completely dependent upon, the vouchers. *See Downs,*870 F.2d at 615; *Wellman,*830 F.2d at 1461 n. 11.

The conviction of Potter rests upon an invoice dated July 21, 1989. She argues that this mailing cannot support her conviction because the mailing preceded any plan to plagiarize her thesis. The record, however, reveals that Frost told Potter in December, 1989 or January, 1990 that she should begin working on her thesis, and that Potter received from Frost or Turner only several months later the FWG report which would be her thesis. Accordingly, a reasonable jury could have concluded that defendants had agreed before the mailing of the invoice that Potter would obtain her degree through plagiarism, and that the invoice therefore furthered the scheme to defraud the government of its payment for her degree.

Potter also argues that the government was not defrauded of any tuition money because, even though she did not write her thesis, she underwent a “legitimate learning experience” by studying the FWG report which she passed off as her thesis. She also insists that NASA frequently pays for its employees merely to take classes, and that she could have taken a non-thesis option when pursuing her master’s degree. Potter, however, ignores the fact that the record easily yields the conclusion that NASA was relieving Potter of her obligation to pay UTSI because it was expecting her to obtain a master’s degree by writing a legitimate thesis. Further, there was evidence that the non-thesis option was not available to Potter, who lacked significant professional engineering experience. NASA did not get what it was paying for simply because Potter attended classes and examined the FWG report.

C. Scheme to Defraud University of Tennessee of Intangible Right to Honest Services of Frost and Turner

Counts Seventeen through Twenty of the Superseding Indictment charged defendants with violating the mail fraud statute by scheming to defraud the University of Tennessee of the “honest services” of Frost and Turner. Specifically, these counts charged that Frost and Turner abused their positions with the University in order to aid the other defendants, who could benefit FWG through their government positions. Essentially, the scheme alleged is that Turner and Frost defrauded the University by allowing each student defendant to pass off material written by others as their own thesis or dissertation, and likewise concealed from the other members of the oral examination committees that the thesis or dissertation under review was not the student’s own work.

The mailings upon which Counts Seventeen through Twenty were based were four memoranda of certification, mailed from UTSI to the University of Tennessee at Knoxville, that the student defendants had passed their oral examinations and were eligible to receive their degrees. The Superseding Indictment charged Frost and Turner as principals under all of these counts and charged each student defendant as an aider and abettor under the count pertaining to the particular memorandum of certification for that student.4 Although the jury acquitted Frost and Turner of Count Eighteen, the count pertaining to Hill, they convicted Frost and Turner of the other counts, and convicted Potter, Faulkner and Congo of the count relating to his or her respective certification mailing.

1. Existence of Doctrine

In *McNally v. United States,*483 U.S. 350, 107 S.Ct. 2875, 97 L.Ed.2d 292 (1987), the Supreme Court reversed a substantial body of precedent previously developed by the federal circuits by holding that the mail fraud statute protected only proper*364ty rights and did not criminalize schemes “designed to deprive individuals, the people, or the government of intangible rights, such as the right to have public officials perform their duties honestly.” *Id.*at 358, 107 S.Ct. at 2881; *see also Carpenter v. United States,*484 U.S. 19, 25, 108 S.Ct. 316, 320, 98 L.Ed.2d 275 (1987)(although, under *McNally,*mail fraud statute does not protect intangible right to honest and faithful service, statute does protect intangible property rights). The *McNally*Court based its holding upon the wording of the mail fraud statute, explaining that the phrase “any scheme or artifice to defraud” was insufficiently clear and definite to justify construing the act so broadly that it would protect an intangible right to honest services. *See McNally,*483 U.S. at 358-60, 107 S.Ct. at 2880-82. Emphasizing that it merely was applying principles of statutory interpretation, the *McNally*Court declared, “If Congress desires to go further, it must speak more clearly than it has.” *Id.*at 360, 107 S.Ct. at 2882.

In 1988, the year following the decision in *McNally,*Congress enacted 18 U.S.C. § 1346. That section provides the following:

> § 1346. Definition of “scheme or artifice to defraud.”

> For the purposes of this chapter, the term “scheme or artifice to defraud” includes a scheme or artifice to deprive another of the intangible right of honest services.

*Id.*

Defendants argue that § 1346 failed to express any clear intent to override the holding in *McNally*and protect intangible rights to honest services under the mail fraud statute. Defendants have relied upon *United States v. Brumley,*79 F.3d 1430 (5th Cir.1996), which held that the term “another” in § 1346 does not include citizens who have been deprived of the honest services of their public officials. Regardless of the fact that defendants were charged with defrauding the University, not the public, of honest services, the Fifth Circuit, sitting *en banc,*has reversed this holding and ruled that the term “another” includes government entities, and that the right to “honest services” includes the right to “honest and impartial government.” *See United States v. Brumley,*116 F.3d 728, 731 (5th Cir.1997)(en banc).

The timing and the explicit terms of § 1346 make clear that Congress intended the provision to reinstate the doctrine of intangible rights to honest services. Every court to address the effect of § 1346 has held that it has overruled the holding in *McNally. See United States v. Czubinski*106 F.3d 1069, 1076 (1st Cir.1997); *United States v. Waymer,*55 F.3d 564, 568 n. 3 (11th Cir. 1995), *cert. denied*— U.S. —, 116 S.Ct. 1683, 134 L.Ed.2d 784 (1996); *see also United States v. Frega,*933 F.Supp. 1536, 1546-47 (S.D.Cal.1996). Further, other circuits, including our own, have observed in dicta that § 1346 has overridden *McNally. See United States v. Bryan,*58 F.3d 933, 940-41 n. 1 (4th Cir.1995); *United States v. Catalfo,*64 F.3d 1070, 1077 n. 5 (7th Cir.1995), *cert. denied,*— U.S. —, 116 S.Ct. 1683, 134 L.Ed.2d 784 (1996); *United States v. DeFries,*43 F.3d 707, 709 n. 1 (D.C.Cir.1995); *United States v. Holley,*23 F.3d 902, 910 (5th Cir.1994); *United States v. Dischner,*974 F.2d 1502, 1518 n. 16 (9th Cir.1992); *United States v. Ames Sintering Co.,*927 F.2d 232, 235 (6th Cir.1990); *United States v. Cranberry,*908 F.2d 278, 281 n. 1 (8th Cir.1990); *United States v. Martinez,*905 F.2d 709, 715 (3d Cir.1990); *see also West Virginia Univ. Hosps., Inc. v. Casey,*499 U.S. 83, 114-15, 111 S.Ct. 1138, 1155-56, 113 L.Ed.2d 68 (1991)(Stevens, J., dissenting)(noting that Congress “quickly corrected” the holding in *McNally).*We therefore hold that § 1346 has restored the mail fraud statute to its pre*McNally*scope, according to previous opinions interpreting the intangible right to honest services. *See, e.g., Czubinski*106 F.3d at 1076; *see also*134 Cong. Rec. H11,108-01 (daily ed. Oct. 21, 1988)(statement of Rep. Conyers)(commenting that § 1346 “is intended merely to overturn the *McNally*decision. No other change in the law is intended”); 134 Cong. Rec. S17,360-02 (daily ed. Nov. 10, 1988)(statement of Sen. Biden)(declaring that the “intent [of § 1346] is to reinstate all of the *pre-McNally*case law pertaining to the mail and wire fraud statutes without change”).

*3652. Application of Doctrine to Non-Public Officials

Frost and Turner next argue that § 1346 does not apply to them because they are not public servants. We reject this argument.

The classic application of the intangible right to honest services doctrine has been to a corrupt public servant who has deprived the public of his honest services. *Cf. United States v. Paradies,*98 F.3d 1266, 1283 n. 30 (11th Cir.1996)(eollecting cases for support of declaration that courts uniformly have construed mail fraud statute as protecting intangible right of citizenry to good and honest government), *cert. denied,*— U.S. —, 117 S.Ct. 2483, 138 L.Ed.2d 992 (1997). The prosecution, however, has charged defendants with depriving the University of Tennessee of its intangible right to the honest services of its employees. Although the University of Tennessee is a public institution, the indictment did not allege that Frost and Turner, acting as public or quasi-public officials, deprived the public of any intangible rights. Likewise, the jury instructions did not refer to Frost or Turner as public officials, but only as employees of the University.5 The liability of defendants therefore depends upon whether § 1346 may apply when a private person breaches a fiduciary duty to his employer.

The wording of § 1346 is very broad: it defines “scheme or artifice to defraud” as including “a scheme or artifice to deprive *another*of the intangible right of honest services.” 18 U.S.C. § 1346 (italics added). Commenting upon this breadth, the Eighth Circuit has stated that “[i]t is certainly true that the literal language of § 1346 extends to private sector schemes to defraud another of the right to ‘honest services.’ ” *United States v. Jain,*93 F.3d 436, 441 (8th Cir. 1996), *cert. denied,*— U.S. —, 117 S.Ct. 2452, 138 L.Ed.2d 210 (1997). However, the *Jain*court also noted that application of the “right to honest services” doctrine to the private sector is problematic. The right of the public to the honest services of its officials derives at least in part from the concept that corruption and denigration of the common good violates “the essence of the political contract.” *See id.*at 442. Enforcement of an intangible right to honest services in the private sector, however, has a much weaker justification because relationships in the private sector generally rest upon concerns and expectations less ethereal and more economic than the abstract satisfaction of receiving “honest services” for their own sake. *See id.*

The *Jain*court declined to answer the questions which it had raised regarding the scope of the intangible right to honest services and instead reversed the mail fraud convictions at issue on other grounds. *See id.*The Sixth Circuit does not appear to have defined the scope of the intangible right to honest services since the passage of § 1346. Accordingly, we must review Sixth Circuit precedent issued before *McNally*in order to discover the precise contours of the right in this circuit.

In *United States v. Gray,*790 F.2d 1290 (6th Cir.1986), *rev’d, McNally v. United States,*483 U.S. 350, 107 S.Ct. 2875, 97 L.Ed.2d 292 (1987), the Sixth Circuit suggested a limited interpretation of the intangible right to honest services doctrine. The *Gray*court explained:

> [T]he “intangible rights” theory is anchored upon the defendant’s misuse of his public office for personal profit. “This doctrine of the deprivation of honest and faithful service has developed to fit the situation in which a public official avails himself of his public position to enhance his private advantage____” *United States v. Dixon,*536 F.2d 1388, 1400 (2d Cir.1976). Conversely, misconduct of a fiduciary in the administration of exclusively private matters in his capacity as a private individual which does not involve the misuse of public office or public trust, is not actionable as a violation of the mail fraud statute under an intangible rights theory. *366*United States v. Rabbitt,*583 F.2d 1014, 1024 (8th Cir.1978), *cert. denied,*439 U.S. 1116, 99 S.Ct. 1022, 59 L.Ed.2d 75 (1979).

*Id.*at 1295. The *Gray*court then adopted the flexible test enunciated in *United States v. Margiotta,*688 F.2d 108 (2d Cir.1982), for whether a defendant is capable of violating the mail fraud act by breaching a fiduciary duty to the public. *Gray,*790 F.2d at 1296. Applying this test, the *Gray*court held that the Kentucky Democratic Party Chairman was a public fiduciary because he “substantially participated in governmental affairs” and exercised significant control over the annual awarding by Kentucky of its workmen’s compensation insurance contract. *See id.*

Subsequent to *Gray*and the decision by the Supreme Court in *McNally,*however, a three-judge panel of the Sixth Circuit decided *United States v. Runnels,*833 F.2d 1183 (6th Cir.1987) *(“Runnels*I”). The government prosecuted the defendant in *Runnels I*in part for having deprived the members of the local union of which he was president of his fair and honest services. *See id.*at 1184. The *Runnels I*court described the intangible right to honest services doctrine before explaining that the recent ruling in *McNally*had invalidated that doctrine. *See id.*at 1185-86. When describing the doctrine, the *Runnels I*court stated that the doctrine not only referred to the intangible right of citizens to fair and honest government, *see id.*at 1185, but also that “[cjourts have ... applied the intangible rights doctrine in corporate and labor cases.” *Id.*at 1186. The *Runnels I*court then provided a string of citations to eases from other circuits in support. *See id.*This dicta suggests that the *Runnels I*court believed that the right to honest services doctrine existing before *McNally*was broader than the language in *Gray*had suggested and generally included deprivations of honest services by private fiduciaries.

The Sixth Circuit later vacated the opinion in *Runnels I*for a rehearing *en banc*and eventually reversed. *See United States v. Runnels,*877 F.2d 481 (6th Cir.1989)(en *banc)(“Runnels II”).*Although the precise issue before the *Runnels II*court was whether the government had indicted and prosecuted the defendant on a theory other than the intangible right to honest services doctrine, the majority in *Runnels II*first discussed the claim asserted by the defendant at trial that the right to honest services theory was “not applicable to this kind of case.” *See id.*at 483. Reciting some of the language from *Gray*quoted *supra,*the *Runnels II*majority acknowledged that the language used in *Gray*“appeared to give support to Runnels’ theory of defense.” *Id.*Nonetheless, the *Runnels II*majority commented upon the denial of the defendant’s motions for new trial and judgment of acquittal by stating that “[t]he trial judge, correctly in our opinion, read *Gray*to have no effect on the doctrine that the intangible rights theory was ‘applicable to non-public officials where a fiduciary duty is involved.’ ” *See id.*at 483-84. Given the fact that Runnels was merely the president of a local union, this statement by the *en banc*court, although dicta, strongly indicates that a private person may violate the mail fraud act by defrauding private parties of their right to his honest services if he owes them a fiduciary duty. Likewise, *Runnels II*indicates that the standard recited in *Gray*is not exclusive, but rather operates only as a test for determining whether an individual owes a fiduciary duty to the public.

We therefore hold that private individuals, such as Frost and Turner, may commit mail fraud by breaching a fiduciary duty and thereby depriving the person or entity to which the duty is owed of the intangible right to the honest services of that individual.

3. Whether Frost and Turner were Fiduciaries of the University

Federal law governs the existence of fiduciary duty under the mail fraud statute. *See Morda v. Klein,*865 F.2d 782, 785 (6th Cir.1989). It is axiomatic that an employee has a fiduciary duty to protect the property of his employer. *See, e.g., Carpenter,*484 U.S. at 27, 108 S.Ct. at 321 (employee has fiduciary duty to protect and not exploit confidential business information of employer); *see generally*Restatement (Second) of Agency § 1 (1958)(defining “agency” as “the fiduciary relation which results from *367the manifestation of consent by one person to another that the other shall act on his behalf and subject to his control, and consent by the other so to act”). A professor therefore owes a fiduciary duty to protect the property of his employer university, just like any other employee. *See Cahn v. Antioch Univ.,*482 A.2d 120, 131-32 (D.C.1984)(deans owed fiduciary duty to university when managing university funds).

Frost and Turner had considerable influence, although not complete control, over whether one of their students received an advanced degree from UTSI. The department of engineering, of which Frost was the Chairman, has only a limited number of graduate students. Further, the major professor of a student has tremendous influence over the direction and ultimate success of that student’s dissertation or thesis, the completion of which is integral to the attainment of an advanced degree. Indeed, Berlinrut testified that he did not graduate from UTSI because Frost gave him a “no progress” for his dissertation research during his last quarter, and because he failed his comprehensive final examination, which Frost prepared by taking the unusual step of not telling Berlin-rut beforehand that the exam would include an additional math problem.

Accordingly, Frost and Turner owed a fiduciary duty to the University when determining whether a student would graduate if the University has a property right in a degree which it has not issued yet. In general, the concept of “property” refers to a “bundle of rights” which includes the rights to possess, use, exclude, profit, and dispose. *See Brotherton v. Cleveland,*923 F.2d 477, 481 (6th Cir.1991). Although we have recognized that a degree is a property interest of the graduate, *see Crook v. Baker,*813 F.2d 88, 98-99 (6th Cir.1987), we also have held that the government does not have a property right in a license which it has not issued yet for the purposes of the mail fraud statute. *See Murphy,*836 F.2d at 253-54; *see also United States v. Kato,*878 F.2d 267, 269 (9th Cir.1989)(under mail fraud statute, unissued pilot license is not property of government); *but see United States v. Salvatore,*110 F.3d 1131, 1139-43 (5th Cir.1997)(unissued video poker license is property of government for purposes of mail fraud). We believe that an unissued university degree differs from an unissued regulatory .license. Ultimately, a university is a business: in return for tuition money and scholarly effort, it agrees to provide an education and a degree. The number of degrees which a university may award is finite, and the decision to award a degree is in part a business decision. Awarding degrees to inept students, or to students who have not earned them, will decrease the value of degrees in general. More specifically, it will hurt the reputation of the school and thereby impair its ability to attract other students willing to pay tuition, as well as its ability to raise money. The University of Tennessee therefore has a property right in its unissued degrees, and Frost and Turner had a fiduciary duty to the University when exerting their considerable influence over whether the school would give a degree to a student.

4. When Breach by Private Fiduciary Violates Mail Fraud Act

The District Court instructed the jury that they could find that Frost and Turner deprived the University of the intangible right to their honest services under the following circumstances:

> What the government must prove is that there was a failure by Walter Frost and Robert Turner to disclose something which in their knowledge or contemplation posed a business risk of harm or loss to their employer, the University of Tennessee. If you find that the nondisclosure of a conflict of interest by Walter Frost and Robert Turner furthered a scheme by them to abuse the trust of their employer in a manner that made an identifiable harm to the University of Tennessee reasonably foreseeable, then you may find that Walter Frost and Robert Turner had the intent to defraud under Section 1341. The key determination is whether you can find from the evidence presented in this ease that Walter Frost and Robert Turner might reasonably have contemplated or understood that the University of Tennessee would suffer some harm to its business *368arising out of or resulting from their failure to disclose their alleged conduct and conflict of interest to the University of Tennessee. However, the government is not required to prove that the intended victim, the University of Tennessee, actually suffered a loss of money or property.

We believe that the above instructions captured the proper standard for determining whether an employee has committed mail fraud by depriving his employer of honest services. The prosecution must prove that the employee intended to breach a fiduciary duty, and that the employee foresaw or reasonably should have foreseen that his employer might suffer an economic harm as a result of the breach. We therefore adopt the standard employed by the District of Columbia Circuit, which holds that an employee deprives his employer of honest services when “the defendant might reasonably have contemplated some concrete business harm to his employer stemming from his failure to disclose the conflict along with any other information relevant to the transaction.” *United States v. Lemire,*720 F.2d 1327, 1337 (D.C.Cir.1983). Proof that the employer simply suffered only the loss of the loyalty and fidelity of the defendant is insufficient to convict. *See id.*

We recognize that the *literal terms*of the “intangible right to honest services” doctrine do not indicate that the prosecution must prove that a fiduciary breach has created a risk of economic harm to the employer. Rather, the literal terms suggest that dishonesty by an employee, standing alone, is a crime. Courts, however, have refused to interpret the doctrine so broadly. For example, the Tenth Circuit has commented that, “[assuming without deciding that § 1346 has application where a private actor or quasi-private actor is deprived of honest services in the context of a commercial transaction, it would give us great pause if a right to honest services is violated by every breach of contract or every misstatement made in the course of dealing.” *United States v. Cochran,*109 F.3d 660, 667 (10th Cir.1997); *see also Czubinski,*106 F.3d at 1077 (when holding that IRS employee who performed unauthorized searches of confidential files did not commit wire fraud, explaining that Congress did not enact § 1346 “to create what amounts to a draconian personnel regulation,” and cautioning against interpreting § 1346 so as to “transform[ ] governmental workplace violations into felonies”); *Jain,*93 F.3d at 442 (stating that “prior intangible rights convictions involving private sector relationships have almost invariably included proof of actual harm to the victims’ tangible interests”). This refusal to carry the intangible rights doctrine to its logical extreme stems from a need to avoid the over-criminalization of private relationships: “[I]f merely depriving the victim of the loyalty and faithful service of his fiduciary constitutes mail fraud, the ends/ means distinction is lost. Once the ends/ means distinction is abolished and disloyalty alone becomes the crime, little remains before every civil wrong is potentially indictable.” *Lemire,*720 F.2d at 1336 n. 11 (quoting John C. Coffee, Jr., *From Tort to Crime: Some Reflections on the Criminalization of Fiduciary Breaches and the Problematic Line Between Law and Ethics,*19 Am.Crim. L.Rev. 117,167 (1981)).

Some courts have attempted to define the reach of the intangible right to honest services doctrine by stating that the misrepresentation or omission at issue must be “material.” *See, e.g., Cochran,*109 F.3d at 667; *United States v. Gray,*96 F.3d 769, 775 (5th Cir.1996), *cert. denied,*— U.S. —, 117 S.Ct. 1275, 137 L.Ed.2d 351 (1997); *Jain,*93 F.3d at 442; *Waymer,*55 F.3d at 571-72; *United States v. Von Barta,*635 F.2d 999, 1006-07 (2d Cir.1980). These courts generally define “materiality” in the context of private activity as existing “whenever ‘an employee has reason to believe the information would lead a reasonable employer to change its business conduct.’ ” *Gray,*96 F.3d at 775 (quoting *United States v. Ballard,*663 F.2d 534, 540 (5th Cir.1981), *modified on other grounds,*680 F.2d 352 (5th Cir.1982 Unit B)). Although the difference between the two standards may be slight, we believe that the “reasonable foreseeability by the employee of potential economic harm to his employer” standard is superior to the “materiality” standard. The standard we adopt for this circuit properly focuses on the intent of the employee, and explicitly acknowledges the *369implicit assumption of the “materiality” standard: “an employer presumably would ‘change its business conduct’ [under the “materiality” standard] only if, upon disclosure of the conflict and any other relevant information, it saw new opportunities for profit or savings, or danger of economic harm____” *Lemire,*720 F.2d at 1338;6*see generally*John E. Gagliardi, Comment, *Back to the Future: Federal Mail and Wire Fraud Under 18 U.S.C. § 1346,*68 Wash. L.Rev. 901, 919-20 (1993)(advocating adoption of reasonable foreseeability of economic harm test). Further, if a “change in business conduct” occurs under the materiality standard when a business alters its behavior merely to avoid the *appearance*of impropriety, rather than a potential economic loss, the intangible right to honest services doctrine may lack substantive limits in the private sector.

Despite the literal terms of § 1346, we therefore have construed the intangible right to honest services in the private sector as ultimately dependent upon the property rights of the victim. Nonetheless, the right to honest services doctrine still applies to a broad range of private conduct. Unlike a defendant accused of scheming to defraud another of money or property, *see infra*Section II.A, a defendant accused of scheming to deprive another of honest services does not have to intend to inflict an economic harm upon the victim. Rather, the prosecution must prove only that the defendant intended to breach his fiduciary duty, and reasonably should have foreseen that the breach would create an identifiable economic risk to the victim. We do not believe that this standard imposes an especially rigorous evidentiary burden upon the prosecution. Further, we stress that we are not reviewing the standard applicable to defendants accused of depriving the public of the honest services of public officials. *See Lemire,*720 F.2d at 1337 n. 13 (noting that court was addressing only private fiduciaries, and suggesting that “[p]ublic officials may be held to a higher standard of public trust; and conflicts of interest may harm the public merely by giving the illusion of unfairness”).

5. Sufficiency of the Evidence

Potter and Congo declare that, even if they plagiarized, they never intended to deprive the University of the honest services of Frost and Turner. As previously explained, however, the record contains considerable evidence that Frost and Turner entered into an intentional scheme with each student defendant in which the professors enabled the student to submit a thesis or dissertation secretly based on plagiarism. Further, the scheme required its participants to deceive the members of the academic committee during the oral defense of the illegitimate paper. The inescapable conclusion is that defendants intended for Frost and Turner to breach the trust which the University had placed in them. Further, the evidence indicates that all defendants intended, much less reasonably contemplated, that the University would suffer a concrete business harm by unwittingly conferring an undeserved advanced degree on each student defendant. Although defendants may not have known that the legal description of their activity would be “scheming to deprive the University of its intangible right to the honest services of its employees,” there is sufficient evidence that all defendants committed or aided and abetted in that crime.

*370We therefore affirm the convictions of each defendant convicted of Counts Seventeen, Nineteen, and Twenty.

D. Constitutional Claims

Congo has mounted a facial challenge to the constitutionality of both § 1341 and § 1346 on the ground of vagueness. In contrast to a claim that a statute is unconstitutional “as applied,” in which a party asserts that application of the statute to his particular circumstances would be unconstitutional, a facial challenge seeks to secure a declaration that a statute is utterly inoperative. *See Ada v. Guam Soc’y of Obstetricians and Gynecologists,*506 U.S. 1011, 1012, 113 S.Ct. 633, 634, 121 L.Ed.2d 564 (1992)(Scalia, J., dissenting), *denying cert. to*962 F.2d 1366 (9th Cir.1992); *see also Hoffman Estates v. Flipside, Hoffman Estates, Inc.,*455 U.S. 489, 494-95, 497, 102 S.Ct. 1186, 1191-92, 71 L.Ed.2d 362 (1982)(assuming that statute does not reach constitutionally protected conduct, facial vagueness challenge will fail unless statute “is impermissibly vague in all of its applications”).

Congo asserts that the phrase “scheme to defraud” in § 1341 is meaningless and renders the Mail Fraud Act impossible to apply intelligently under any circumstances. Although several opinions have addressed and rejected claims that Act was impermissibly vague as applied,7 only a few courts have decided facial challenges, and none have invalidated the Act. We agree with the Second Circuit, which, in rejecting a facial challenge to § 1341, explained:

> Section 1341 has withstood repeated challenges which have raised the claim that it does not provide fair notice and warning of the conduct proscribed by the statute. The broad language of the statute, intended by Congress to be sufficiently flexible to cover the wide range of fraudulent schemes mankind is capable of devising, is not unconstitutionally vague because § 1341 contains the requirement that the defendant must have acted willfully and with a specific intent to defraud.

*Margiotta,*688 F.2d at 129 (citation omitted). Indeed, the law traditionally has conceived of “fraud” in general as a necessarily fluid concept; as one court has observed, fraud “is as old as falsehood and as versable as human ingenuity.” Weiss *v. United States,*122 F.2d 675, 681 (5th Cir.1941). “That there may be marginal eases in which it is difficult to determine the side of the line on which a particular fact situation falls is no sufficient reason to hold the language too ambiguous to define a criminal offense.” *United States v. Petrillo,*332 U.S. 1, 7, 67 S.Ct. 1538, 1542, 91 L.Ed. 1877 (1946). Moreover, the case law provides innumerable illustrations of how an individual clearly may perpetrate a “scheme to defraud,” *see, e.g., Carpenter,*484 U.S. at 28, 108 S.Ct. at 321-22 (unanimous Court found “little trouble” in finding that scheme to trade on confidential business information constituted mail fraud); *United States v. Jackson,*72 F.3d 1370, 1386 (9th Cir.1995)(acts of mail fraud and other violations provided a “clear and extreme case of corruption”), cer*t. denied,*— U.S. -, 116 S.Ct. 1546, 134 L.Ed.2d 649 (1996), thereby belying the claim that § 1341 has no valid application.

Congo also argues that § 1346 is facially unconstitutional due to vagueness. He stresses that, in *Carpenter,*484 U.S. at 25, 108 S.Ct. at 320, the Supreme Court described the previous opinion in *McNally*as holding that the right to honest and faithful services was too “ethereal” to fall within the scope of the mail fraud statute. Both the *Carpenter*and the *McNally*Courts, however, found the intangible right to honest services too “ethereal” only when compared to the perceived intent of Congress — “the desire to protect individual property rights.” *Carpenter,*484 U.S. at 25, 108 S.Ct. at 320 (quoting *McNally,*483 U.S. at 359 n. 8, 107 S.Ct. at *3712881 n. 8). Likewise, and as we already have explained, *see supra*Section II. C, the holding in *McNally*represents a decision regarding statutory interpretation, *not*constitutional law.

We already have explained that the enactment of § 1346 intended to restore opinions predating *McNally*and interpreting the intangible right to honest services. These opinions explain that this right is the right to the honest services of a public or private fiduciary, and that private fiduciaries deprive another of honest services when they, during a scheme of intentional deception, breach their fiduciary duties and reasonably do or should foresee that this breach will inflict an identifiable economic harm upon the person or entity to whom they owe their duty. The contours of § 1346 therefore are sufficiently clear for us to conclude that the statute is not unconstitutionally vague on its face. *See United States v. Sawyer,*878 F.Supp. 279, 290-91 (D.Mass.1995)(§ 1346 not “impermissibly vague ‘in all of its applications’ ”), *rev’d on other grounds,*85 F.3d 713 (1st Cir.1996); *see also Paradies,*98 F.3d at 1282-83 (§ 1346 not vague as applied to defendants at issue); *Bryan, 58*F.3d at 941-42 (holding the same); *Waymer, 55*F.3d at 568-69 (rejecting as-applied vagueness and facial overbreadth challenges to § 1346); *United States v. Frego,*933 F.Supp. 1536, 1547 (S.D.Cal.1996)(§ 1346 valid as applied).

Congo, joined by his codefendants, also argues that an instruction delivered in this case allowed the jury to convict on the basis of an unconstitutionally vague definition of mail fraud.8

We reject this claim. The jury instructions provided in part:

> Section 1341 makes it a crime to knowingly devise both a scheme to defraud and a scheme to obtain money or property by false or fraudulent pretenses, representations, or promises____ These are two separate ways that a person can commit mail fraud.

> “Fraud” is an intentional or deliberate misrepresentation of the truth for the purpose of inducing another to part with a thing of value or to surrender a legal right. Fraud, then, is a deceit which; whether perpetrated, by words, conduct, or silence, is designed to cause another to act upon it to its legal injury. A statement, claim or document is “fraudulent” if it was falsely made, or made with reckless indifference as to its truth or falsity, and made or caused to’ be made with an intent to deceive.

> The phrases “any scheme or artifice to defraud” and “any scheme or artifice for obtaining money or property” mean any deliberate plan of action or course of conduct by which someone intends to deceive or cheat another or by which someone intends to deprive another of something of value. *A scheme or artifice to defraud may describe a departure from fundamental honesty, moral uprightness, or fair play and candid business dealings in the general life of the community.*There must be proof of either a misrepresentation, false statement, or omission calculated to deceive a person of ordinary prudence and comprehension.

> A scheme to defraud may occur in violation of Section 1341 even absent a false statement or false representation, and may be based on. fraudulent omissions. A scheme to defraud includes the knowing concealment of facts and information done with the intent to defraud.

> The key issue in this case is whether the defendants had intent to defraud____ To act with “intent to defraud” means to act knowingly and with the intention or the purpose to deceive or cheat. An intent to defraud is accompanied, ordinarily, by a desire or purpose to bring about some gain or benefit to oneself or some other person or by a desire or a purpose to cause some loss to some person.

Focusing on the highlighted sentence, Congo argues that the instructions allowed the *372jury to convict defendants simply for having violated such vague standards as “fundamental honesty” or “moral uprightness.”9 The disputed language, however, occurred in the context of the detailed instructions quoted above, which, as a whole, provided that the jury could not convict defendants merely for not having acted according to fundamental honesty or moral uprightness. Moreover, we observe that the Sixth Circuit already has approved the language of which the defendants complain. *See United States v. Stull,*743 F.2d 439, 445 n. 7, 445-46 (6th Cir.1984).

E. Failure to Instruct on Theory of Potter’s Defense

Potter requested the following jury instruction regarding her theory of the defense:

> Defendant Peggy Potter says that she followed the instructions of her major professor, Dr. Frost in the preparation of her thesis.. Even if the thesis fails to meet technical academic standards of originality the courses itself [sic] was a suitable project and a suitable learning experience satisfying the educational requirements of NASA. She had no intent to deprive the University of Tennessee of the honest services of Drs. Frost and Turner as alleged in Count 17.

> She had no intent to defraud NASA and had no part in the mailing of the invoice for payment of her courses nor did she induce anyone to mail this invoice as set out in Count 8 of the indictment.

> She had nothing to do with the mailing of vouchers 9 through 12, which were vouchers on a contract unrelated to her.

> She did not favor Dr. Frost or FWG in exchange for any favors and had no agreement to do so.

Although the District Court declined to give the above charge, it did instruct the jury in detail that a defendant must possess the intent to defraud in order to violate the mail fraud statute, and that good faith on the part of a defendant is inconsistent with an intent to defraud. Further, the court properly instructed the jury that the government must prove that the mails furthered the alleged scheme, and that the use of the mails by someone was reasonably foreseeable, but not that a defendant actually intended to use the mails or actually mailed something herself. *See, e.g., Oldfield,*859 F.2d at 400. The court also instructed the jury that “[plagiarism, and having someone else write your thesis or dissertation for you, are not, standing alone, mail fraud.”

“We review jury instructions as a whole to determine whether they fairly and adequately submitted the issues and applicable law to the jury.” *United States v. Williams,*952 F.2d 1504, 1512 (6th Cir.1991). “A ... refusal to deliver a requested instruction is reversible only if that instruction is (1) a correct statement of the law, (2) not substantially covered by the charge actually delivered to the jury, and (3) concerns a point so important in the trial that the failure to give it substantially impairs the defendant’s defense.” *Id.*Even if only weak evidence supports the requested instruction, it is reversible error in a criminal case not to give an adequate presentation of a theory of defense. *See United States v. Newcomb,*6 F.3d 1129, 1132 (6th Cir.1993).

The ultimate weakness of the instructions requested by Potter is that they consist primarily of factual arguments. Rather than articulating a distinct legal theory, they merely assert that Potter did not violate the intent and mailing requirements already described by the District Court.10 It is not error to refuse to give special instructions which merely represent a defendant’s view of the facts of the ease. *See United States v. Warner,*971 F.2d 1189, 1203 (6th Cir.1992); *cf. United States v. Carr, 5*F.3d 986, 992 (6th Cir.1993)(no error not to instruct specifically the jury on alleged inherent lack of credibility of certain witnesses).

*373Finally, there is no indication in the record that Potter objected to the instructions as given, and Potter does not claim in her brief to have done so. Because Potter did not object to the final jury instructions, we review for plain error under Fed.R.Crim.P. 52(b). Under Rule 52(b), any error committed by the District Court was not “plain” because it continues to remain unclear whether Potter was mounting a good-faith reliance defense, the only specific legal theory perhaps not covered by the instructions given. *See United States v. Olano,*507 U.S. 725, 734, 113 S.Ct. 1770, 1777-78, 123 L.Ed.2d 508 (1993)(“plain” error is one that is “clear” or “obvious”). Further, given the evidence refuting the claim of Potter that she honestly believed that plagiarizing her thesis was an acceptable method of obtaining her degree, we do not believe that any error here could have “seriously affeet[ed] the fairness, integrity, or public reputation of judicial proceedings.” *See id.*at 732, 113 S.Ct. at 1776.

III. Claims Concerning Deliberative Process of Jury

A. *Allen*Charge

Because the jury had indicated that it was having difficulty reaching a verdict on some of the counts, the District Court delivered a supplemental instruction designed to encourage the jury to reach a verdict by requesting each juror to reconsider his or her respective position during continued deliberations. Such a charge is often referred to as an *Allen*charge, named after *Allen v. United States,*164 U.S. 492, 17 S.Ct. 154, 41 L.Ed. 528 (1896), in which the Supreme Court approved the use of such an instruction. Defendants argue that they must receive new trials because the *Allen*charge delivered in this case coerced an otherwise deadlocked jury into rendering its verdicts.

We review a decision to give an *Allen*charge only for abuse of discretion, *see United States v. Tines,*70 F.3d 891, 896 (6th Cir.1995), *cert. denied,*— U.S. -, 116 S.Ct. 1280, 134 L.Ed.2d 225 (1996), because “the presiding judicial officer is in the best position to decide when to give the charge____” *United States ¶. Sawyers,*902 F.2d 1217, 1220 (6th Cir.1990). We must examine whether, “in its context and under all the circumstances, [the charge] ... was coercive.” *United States v. Aloi,*9 F.3d 438, 443 (6th Cir.1993)(quoting *Williams v. Parke,*741 F.2d 847, 850 (6th Cir.1984)(quoting *Jenkins v. United States,*380 U.S. 445, 446, 85 S.Ct. 1059, 1060, 13 L.Ed.2d 957 (1965))).

The District Court gave the *Allen*charge under the following circumstances. The trial began on March 28, 1995, and continued for approximately one month. On April 24, 1995, a Monday, counsel delivered their closing arguments and the District Court gave final instructions to the jury. The jury deliberated for one hour on April 24 and resumed ,its deliberations on April 26, a Wednesday. At 3:30 p.m. on April 26, the jury sent a note to the District Court which asked, “What if we cannot reach a unanimous decision on all counts concerning one defendant?” The District Court responded with a written note which stated, “Please continue to deliberate and attempt, to reach a unanimous verdict on all counts.”

The jury continued to deliberate on April 27. At 2:45 p.m. on April 27, it sent another written communication to the District Court, stating “Two defendants — Reach verdicts on some counts. Two counts per defendant. Deadlock on other counts concerning them. Please advise.” The District Court again responded in writing, stating: “If you have done everything you can do with respect to two defendants, please consider the cases against the other defendants.” At 4:45 p.m., the jury indicated to the District Court that it wished to resume deliberating the next day.

Accordingly, the jury returned on April 28, a Friday. That morning, the jury notified the District Court that a juror named Shelby had brought a newspaper article and some personal notes from her home into the jury room. After advising counsel of this fact, the District Court interviewed Shelby *in camera*in the presence of a court reporter; although it is unclear whether all counsel also were present during the interview, at least counsel for Frost and the government were present. The transcript of the interview reveals that the District Court tactfully reminded Shelby *374that it had instructed her not to rely upon anything when deciding this case other than the evidence presented. Further, the District Court established that the article was not about the case itself, but an issue raised by the case, and that Shelby had prepared her notes solely from memory. Shelby also asserted that the other jurors had not read the article or her notes, and that the article would not influence her decision-making. Shelby attempted to explain why she had compiled the notes by blurting out, “I felt a little maybe outnumbered, and I felt like I needed for my personal justification of the way I believe____” She stopped explaining, however, after the District Court interjected, “We don’t want to get into that.” After verifying that counsel had no questions, the District Court allowed Shelby to return to the jury room but retained her article and notes, making them a court exhibit. According to the District Court in its July 13, 1995 memorandum denying defendants’ motion for new trial, “it became obvious through her personal notes that Shelby was generally favorable to the defense.” The District Court rejected a request by government counsel to disqualify Shelby from the jury.

At about 2:15 p.m. on April 28, the jury sent another written message to the judge, stating that “we have reached a verdict on some counts but cannot seem to on the others. Please advise.” At that point, the District Court, over the objections of defendants, decided to give Sixth Circuit Pattern Criminal Jury Instruction 9.04, an instruction intended for deadlocked juries which tracks but does not duplicate the instruction in *Allen.*11

At 4:15 p.m. that day, the jury returned a unanimous verdict; the jury found all defendants guilty of every count with which he or she had been charged, except that it found Frost and Turner not guilty of Count Eighteen, and found Turner not guilty of Count Thirty. When the District Court polled the jury, every juror responded that he or she concurred in the verdict.

Appropriately, defendants do not contest the wording of the *Allen*charge given by the District Court. The pattern instruction delivered in this case contained language which *375this circuit has identified as critical to any *Allen*charge: it directed both majority and minority jurors to reconsider their positions, *see, e.g., Williams,*741 F.2d at 850, and it cautioned all jurors not to surrender their personal convictions merely in order to achieve consensus by acquiescing in the majority opinion. *See, e.g., Aloi,*9 F.3d at 443; *United States v. Nickerson,*606 F.2d 156, 159 (6th Cir.1979). Defendants instead argue that the charge, although properly worded, was nonetheless coercive under the particular circumstances of this case. Although circumstances alone can render an *Allen*charge coercive, we traditionally have found an *Allen*charge coercive when the instructions themselves contained errors or omissions, not when a defendant alleges that the circumstances surrounding an otherwise correct charge created coercion. *See United States v. Scott,*547 F.2d 334, 337 (6th Cir.1977)(trial court failed to remind jury that no one should surrender honest beliefs simply because others disagreed, and suggested that continued disagreement would interfere unacceptably with commencement of pending civil trial); *Jones v. Norvell,*472 F.2d 1185, 1185 (6th Cir.1973)(per curiam)(trial court told jury that they were “the only ones” who could reach a verdict); *United States v. Harris,*391 F.2d 348, 352-53 (6th Cir.1968)(trial court told minority to consider views of majority, but not vice-versa).

We find that, under all of the circumstances, the District Court did not abuse its discretion by delivering an *Allen*charge. Defendants emphasize that the District Court knew at the time of the charge that juror Shelby was favoring the defense and was in the minority. They further stress that Shelby knew that the District Court knew of her position. Defendants rely upon *United States v. Sae-Chua,*725 F.2d 530 (9th Cir.1984), in which

> the court found that a lone dissenter who favored acquittal was unduly pressured by the [trial] court’s supplemental instruction. The circumstances in *Sae-Chua*include that the jury foreperson reported which way the verdict was split (eleven in favor of conviction, one for acquittal) and accused the dissenter of having improperly stated that he believed the defendant was guilty but would not vote for, conviction. The judge polled the jury and it became clear which juror was the dissenter. It was in this context that the court of appeals found that the dissenting juror must have felt he was targeted by the judge to reconsider his vote.

*United States v. Lash,*937 F.2d 1077, 1085-86 (6th Cir.1991)(deseribing Sae-Chua). Unlike in *Sae-Chua,*however, the trial court in the instant ease did not know whether Shelby was the lone dissenter, and Shelby knew that the trial court did not know. Similarly, the District Court did not know whether Shelby was leaning towards the defense or was in the minority with regards to each defendant and each count. Further, the coercive pressures exerted in *Sae-Chua*by the open accusation of the foreperson that the sole dissenter was engaging in misconduct, as well as the trial court’s decision to poll the jury, do not exist here. For these reasons and the reasons explained *infra,*we do not believe that the District Court abused its discretion or that *Sae-Chua*controls.

Another factor indicating a lack of coercion is that Shelby volunteered the information that she was in the minority and was leaning towards the defense. “Where the jury has disclosed the split voluntarily and the instruction has not focussed on the minority, courts have generally upheld [an *Allen*charge].” *Lash,*937 F.2d at 1086. In *Lash,*we found that the trial court did not abuse its discretion by giving an *Allen*charge in part because it had learned of the numerical split of the jury only inadvertently. *See id.*Although *Lash*differs from this case to the extent that the *Lash*jury did not reveal the particular position of the minority or the identity of any minority juror, see *id., Lash*also contains evidence of coercion not present here:, a juror in *Lash*sent a note to the trial court asking to be excused.. *See id.**12***Fur*376ther, *Lash*cited with approval three cases from other circuits approving an *Allen*charge even though the trial court had learned that the jury was split eleven-to-one in favor of conviction. *See id.*(citing *United States v. Gabriel,*597 F.2d 95, 100 (7th Cir.1979); *United States v. Robinson,*560 F.2d 507, 517 (2d Cir.1977); *Sanders v. United States,*415 F.2d 621, 629-31 (5th Cir.1969)).

Stressing that lengthy jury service may render a jury minority particularly susceptible to coercion, *see Williams,*741 F.2d at 850-51, defendants note that the jury had been deliberating for approximately three days after a month-long trial. The length of the deliberations in this case, however, is not particularly significant, given the fact that the jury had a tremendous amount of information to process (witness the length of this opinion) in order to decide thirty-one counts in a complicated case involving five defendants. Further, the jury notes sent on April 27 and 28, which revealed that the jury was unanimous as to some counts for some defendants, showed that the jury, including Shelby, had reached agreement on at least part of the case by working together during deliberations, not remaining in deadlocked stasis. Although we have observed that “an *Allen*charge coming relatively early is arguably less coercive than one coming after a jury has worn itself out after several days of deadlocked deliberations,” *Sawyers,*902 F.2d at 1220, the circumstances of this case do not compel the conclusion that a tired minority finally acceded to the majority opinion in the face of an *Allen*charge delivered after days of emotionally difficult deadlock.

Finally, defendants invoke *United States v. Ford (In re Ford),*987 F.2d 334 (6th Cir.1992), in which we held that the trial court had not abused its discretion by not giving an *Allen*charge but instead declaring a mistrial. *See id.*at 339-41. In *Ford,*however, the jury had deliberated for four days and had indicated on two occasions, once after two days of deliberations and once immediately preceding the declaration of mistrial, that it was “hopelessly deadlocked.” *See id.*at 340. Further, the jury disclosed both its precise numerical split and the position of its majority by revealing that it was split eight to four in favor of acquittal. *See id.*Moreover, the jury had not reached agreement as to *any*of the defendants or *any*of the charges at the time of the mistrial declaration, even though the trial court had instructed it that it could return a partial verdict. *See id.*Most importantly, *Ford*did not hold that the above facts *precluded*an *Allen*charge, but that they allowed the trial court to refuse to give an *Allen*charge. *See id.*Ultimately, the *Ford*opinion highlights the discretion accorded to trial courts.13

B. *Remitter*Hearing

After the jury rendered its verdicts on April 28, a juror approached the mother of Congo in the courthouse parking lot and informed her that juror Shelby had left the jury room during the afternoon of that day with the assistance of an unidentified deputy court clerk in order to lie down for about twenty minutes in the Clerk’s office because she had been feeling ill from chest pains. Defendants subsequently moved for an evidentiary hearing on whether Shelby had been exposed to prejudicial external influences during her absence from the jury room; Congo attached to his motion the affidavit of his mother, in which she related the *377above incident in the courthouse parking lot. The District Court, which never knew at the time that Shelby had left the jury room to lie down, denied the requests for a hearing.14 Defendants now assert that this denial of a hearing was improper and requires new trials.

In *Remmer v. United States,*347 U.S. 227, 74 S.Ct. 450, 98 L.Ed. 654 (1954), the Supreme Court held that because juries in criminal eases must be free from outside influences, a trial court confronted with an allegation of external tampering or contact with a juror during trial about a matter pending before the jury “should determine the circumstances, the impact [of the contact] upon the juror, and whether or not it was prejudicial, in a hearing with all interested parties permitted to participate.” *United States v. Rigsby,*45 F.3d 120, 123 (6th Cir.(quoting *Remmer,*347 U.S. at 230, 74 S.Ct. at 451), *cert. denied,*514 U.S. 1134, 115 S.Ct. 2015, 131 L.Ed.2d 1013 (1995). Nonetheless, “not all communications with jurors warrant a hearing for a determination of potential bias.” *Id.*at 124 (quoting *White v. Smith,*984 F.2d 163, 166 (6th Cir.1993)). Instead, an allegation of an unauthorized communication with a juror requires a *Remmer*hearing only when the alleged contact presents a likelihood of affecting the verdict. *See id.*at 123. Accordingly, we generally have required trial courts to conduct *Remmer*hearings only in eases involving claims of “intentional improper contacts or contacts that had an obvious potential for improperly influencing the jury.” *Id.*at 124. Further, the defendant must show that an unauthorized contact created actual juror bias; courts should not presume that a contact was prejudicial. *See, e.g., United States v. Walker,*1 F.3d 423, 431 (6th Cir.1993); *United States v. Zelinka,*862 F.2d 92, 95-96 (6th Cir.1988); *United States v. Pennell,*737 F.2d 521, 530-32 (6th Cir.1984). We review a decision by a trial court not to hold a *Remmer*hearing for abuse of discretion. *See Rigsby,*45 F.3d at 125; *United States v. Griffith,*17 F.3d 865, 880 (6th Cir.1994).

In the instant case, the District Court did not abuse its discretion by refusing to hold a *Remmer*hearing because defendants presented no basis upon which to believe that Shelby even had experienced an external contact or communication regarding matters pending before the jury during her absence from the deliberations. The need for a *Remmer*hearing necessarily does not arise absent the existence of an outside influence on a juror, see *Rigsby,*45 F.3d at 125; *Griffith,*17 F.3d at 880, and the record here suggests only that Shelby retired to a couch in the Clerk’s office to lie down for about twenty minutes, not that she ever encountered any external influence pertaining to this case during that period.

Defendants, however, argue that the District Court improperly denied them any opportunity to discover exactly what Shelby did during her absence. Defendants cite *United States v. Shackelford,*777 F.2d 1141, 1144-45 (6th Cir.1985), in which we upheld a decision not to grant an evidentiary hearing when a juror had left deliberations and spoke with his wife for a few minutes before returning. Although we found that the defendants in *Shackelford*had failed to show that the juror had been exposed to any extraneous information which could have prejudiced them because the juror always had voted for guilt since the beginning of deliberations, *see id.*at 1145, defendants here emphasize that the trial court in *Shackelford*at least had allowed defense counsel to interview the jurors before denying the motion for an evidentiary hearing. *See id.*Defendants claim that the holding in *Shackelford*rests upon this fact, and complain that the Local Rules of the Eastern District of Tennessee allow counsel *378to interview jurors only with permission, which the District Court did not grant in this case. Defendants, however, could have tried to discover what happened to Shelby during her absence simply by talking to staff members of the Clerk’s office. Accordingly, the District Court had no duty to hold a hearing on whether Shelby even experienced an external communication regarding matters pending before the jury, much less whether a given external contact was prejudicial.

During oral argument, counsel argued that reversal is required because- the District Court did not instruct the jury to stop deliberating during the absence of Shelby. Defendants, however, have not submitted any evidence from nonjuror sources regarding the absence of Shelby, but instead rely upon the affidavit of Congo’s mother, not included in the joint appendix, in which the only information regarding the absence of Shelby is a reiteration of a statement about her absence made by another juror.

Defendants have confined themselves in their briefs to arguing that the absence of Shelby is an issue only because external forces may have prejudiced her. Defendants apparently have recognized that the Congo affidavit provides only a limited basis upon which to attack the verdicts because it is based upon a juror statement.

Federal Rule of Evidence 606(b) states:

> Upon an inquiry into the validity of a verdict or indictment, a juror may not testify as to any matter or statement occurring during the course of the jury’s deliberations ..., except that a juror may testify on the question of whether extraneous prejudicial information was improperly brought to the jury’s attention or whether any outside influence was improperly brought to bear upon any juror. Nor may a juror’s affidavit or evidence of any statement by the juror concerning a matter about which the juror would be precluded from testifying be received for these purposes.

Fed.R.Evid. 606(b). The Advisory Committee Notes to Rule 606(b) reveal that Congress rejected a proposed deletion which would have allowed challenges to verdicts “on the basis of what happened during the jury’s internal deliberations, for example, where a juror alleged that the jury refused to follow the trial judge’s instruction or that some of the jurors did not take part in deliberations.” Fed.R.Evid. 606(b) advisory committee’s note.

Rule 606(b) therefore prohibits an inquiry based upon evidence provided by a juror into the effect of the absence of Shelby upon the deliberative process, unless that evidence concerns an external prejudicial influence. *See Tanner v. United States, 483*U.S. 107, 127, 107 S.Ct. 2739, 2751, 97 L.Ed.2d 90 (1987)(Rule 606(b) barred jury testimony of drug use by other jurors during deliberations; in general, possibility of nonjuror evidence of jury misconduct sufficiently protects Sixth Amendment interests); *Shackelford,*777 F.2d at 1145 (upholding refusal to hold evidentiary hearing on absence of juror during deliberations; because jury members already had stated that outside forces had not influenced them improperly, Rule 606(b) barred further testimony); *United States v. Camacho,*865 F.Supp. 1527, 1534-37 (S.D.Fla.1994)(Rule 606(b) barred evidence that juror was absent from jury room during deliberations, including when jury determined final verdict); *see also Tines,*70 F.3d at 898 (Rule 606(b) barred consideration of juror affidavit outlining jury misconduct; effect of *Allen*charge upon jury did not constitute “outside influence”).

C. Juror Bias

Turner asserts that the District Court erred by not declaring a mistrial or excusing a juror when she became a witness to his credibility. The other defendants argue that the District Court should have severed Turner from the trial once the juror at issue became biased. We reject these claims for the following reasons.

After Turner finished testifying on April 20, 1995, juror Golson reported to the District Court that Turner had stated “you all take care of me” to the jury as he left the witness stand. When defense counsel later asked Turner what had happened, Turner responded that he instead had stated, “I hope I don’t trip again,” thereby referring *379to an incident during Ms testimony the preceding day, when he had tripped either ascending or descending the witness stand. Defense counsel also interviewed the court reporter, who, according to defense counsel, verified that she thought that Turner had said what he claimed to have said.

The next day, the District Court interviewed Golson alone in chambers. The following exchange occurred:

> Court: Okay. Now, my question to you is what did you hear, if anytMng, Dr. Turner say?

> Golson: He said you all take care of me.

> Court: Let me ask you this. Do you know if any other juror heard that?

> Golson: They didn’t understand what he said, but they heard him mumble. I heard it plainly.

> Court: Okay. Now, could he have said something like I hope I don’t trip again or something like that? Do you remember when he got up on the stand there?

> Golson: Yes.

> Court: When he started to get up there. And could he have made some statement like that do you think?

> Golson: No.

Golson informed the District Court that she had reported what Turner said because she had been instructed to report any communications from parties or witnesses. She further assured the court that nothing Turner had said would affect her ability to make a fair decision in the case, and that she understood that what Turner had said was not evidence. Finally, Golson told the District Court that four other jurors had heard her report what she thought Turner had said.

The District Court thereafter interviewed individually the other four jurors identified by Golson, and determined that none of these four jurors heard what Turner had said, although they did hear him mumble something. Three of the jurors, however, did hear Golson say what she thought Turner had said. The District Court denied a motion by Turner for mistrial or to disqualify Golson. The other defendants did not want Golson removed, but instead moved without success to sever Turner from the case and continue the trial with the jury constituted as is, but without Turner.

Under the Sixth Amendment, a defendant has the right to be tried by impartial and unbiased jurors. *See, e.g., Ross v. Oklahoma,*487 U.S. 81, 85, 108 S.Ct. 2273, 2276-77, 101 L.Ed.2d 80 (1988). Turner asserts that this right was violated because Golson became a witness as to his credibility. Turner argues that “it is unrealistic for a juror to repeat an alleged comment, be confronted as was Ms. Golson with a different version, and not expect that the juror would see that her story was disputed by the very person she was sitting in judgment upon.”

Neither we nor the parties have located precedent similar to this case. Turner stresses that Federal Rule of Evidence 606(a) bars a juror from testifying before the jury in the trial in which the juror is sitting. Strictly speaking, however, Rule 606(a) does not apply here simply because Golson was not called as a witness. Rule 606(a) nonetheless underscores the importance of the general principle at issue here, the right to an impartial jury.

Turner argues that we must infer the existence of juror bias under these circumstances. The doctrine of presumed or implied, as opposed to actual, bias provides that, in' certain “extreme” or “exceptional” cases, courts should employ a conclusive presumption that a juror is biased. *See McDonough Power Equip., Inc. v. Greenwood,*464 U.S. 548, 556-57, 104 S.Ct. 845, 850-51, 78 L.Ed.2d 663 (1984)(Blackmun, J., concurring); *id.*at 558, 104 S.Ct. at 851 (Brennan, J., concurring); *Smith v. Phillips,*455 U.S. 209, 221-24, 102 S.Ct. 940, 948-50, 71 L.Ed.2d 78 (1982)(O’Connor, J., concurring); *id.*at 231, 102 S.Ct. at 953 (Marshall, J., dissenting); *Hunley v. Godinez,*975 F.2d 316, 318-20 (7th Cir.1992); *Tinsley v. Borg,*895 F.2d 520, 526-29 (9th Cir.1990). These extreme cases occur when a juror has “a relationsMp in which the ‘potential for substantial emotional involvement, adversely affecting impartiality,’ is inherent[.]” *Tinsley,*895 F.2d at 527 (quoting *United States v.**380*Eubanks,*591 F.2d 513, 517 (9th Cir.1979)); *see also Hunley,*975 F.2d at 319 (courts presume bias when a juror “is connected to the litigation at issue in such a way that [it] is highly unlikely that he or she could act impartially during deliberations”); *Person v. Miller,*854 F.2d 656, 664 (4th Cir.1988)(holding the same). For example, one court has presumed bias when a juror sitting in a murder trial in which the defense was battered-wife syndrome was herself the victim of domestic abuse. *See Burton v. Johnson,*948 F.2d 1150, 1159 (10th Cir.1991). Conversely, courts have refused to imply bias when a juror was personally acquainted with a witness, *see Tinsley,*895 F.2d at 528-29 (collecting cases), or when the employment of a juror is closely related to the substance of the trial. *See id.*at 529 (no implied bias in rape prosecution when social worker juror had counselled rape victim for eighteen months and testified on her behalf). Further, the Sixth Circuit has declined to presume bias when a juror unintentionally failed to divulge during voir dire that she was related to a law enforcement officer, and another juror unintentionally failed to disclose the fact that she and her family had previous contacts with the defendants and their families. *See United States v. Howard,*752 F.2d 220, 223-25, *aff'd on rehearing,*770 F.2d 57 (6th Cir.1985)(en banc); *see also Walker,*1 F.3d at 431; *Pennell,*737 F.2d at 530-32 (no presumption of bias when third-party communicates with juror).

The Supreme Court has never held explicitly that courts may infer or presume bias. *See Dyer v. Calderon,*113 F.3d 927, 938 (9th Cir.1997); *see also Howard,*752 F.2d at 223-24 (discussing but declining to decide whether majority opinions by Supreme Court in *McDonough*and *Phillips, supra,*have overruled doctrine of implied bias). Assuming that courts sometimes may, *cf. Cox v. Treadway,*75 F.3d 230, 239 (6th Cir.)(rejecting claim that family relationship of juror with law enforcement agents was basis for causal challenge during voir dire due to implied bias), *cert. denied,*— U.S. —, 117 S.Ct. 78, 136 L.Ed.2d 37 (1996), we find that the doctrine of implied bias does not apply in this case.15 The mere fact that the District Court asked Golson if Turner actually may have said something other than what she thought he had said hardly compels the conclusions that Golson would assume that Turner was contesting her version of events *and*therefore would become incapable of remaining impartial. Although Turner notes that Justice O’Connor has suggested that courts might presume bias when a “juror was a witness or somehow involved in the criminal transaction,” *see Phillips,*455 U.S. at 222, 102 S.Ct. at 948 (O’Connor, J., concurring), this statement simply does not apply to Golson, who did not witness the events giving rise to these prosecutions.

Having found that the doctrine of implied bias does not apply, we review the finding of impartiality by the District Court for abuse of discretion, bearing in mind that Turner bears the burden of proving bias. *See Howard,*752 F.2d at 225; *cf. Clemmons v. Sowders,*34 F.3d 352, 355 (6th Cir.1994)(decision to excuse prospective juror for cause reviewed for abuse of discretion). The District Court interviewed Golson and believed her assertions of continued impartiality to be credible, which the court was entitled to do. *See, e.g., United States v. Rugiero,*20 F.3d 1387, 1390 (6th Cir.1994). Turner has presented no evidence to rebut this finding of credibility. Further, the District Court did not err by dismissing as speculation Turner’s insistence that Golson knew that he had denied her version of events. To the extent that Turner is arguing that Golson could not remain impartial because she believed that Turner improperly had requested help from the jury, it was within the discretion of the District Court to find that Golson remained impartial because the comment that she had heard was “neither inculpatory nor exculpatory in nature,” and “although improper, relatively innocuous.”

*381As noted, the other defendants claim that the District Court erred by denying their motions to sever Turner from their cases once Golson became biased against him and rejected his credibility. Because the District Court did not err by finding that Golson remained impartial, however, this argument necessarily fails.

IV. Remaining Issues

A. *Brady*Violation

Frost contests the sufficiency of the evidence for Counts Twenty-Five through Twenty-Nine, which allege that he fraudulently charged the government for employee bonuses by billing the bonuses as “direct” expenses under FWG contracts, when in fact Frost either should have billed them as “indirect” expenses or not billed them at all. Alternatively, Frost argues that these convictions must be reversed because the government violated its obligation under *Brady v. Maryland,*373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), by failing to disclose exculpatory evidence material to these counts. Frost finally argues that he at least should receive an evidentiary hearing on his *Brady*claim.

The government alleges in Counts Twenty-Five through Twenty-Nine that Frost submitted five vouchers charging the government for about $65,000 in bonuses awarded to himself and four other FWG employees under different FWG contracts. The government claims that these vouchers were fraudulent because Frost knowingly failed to comply with applicable federal regulations which required him to have a bonus plan in place before billing the government for any bonuses, and to provide notice that he was charging for bonuses. The government also argues that, even if Frost could have charged for bonuses, he falsely labelled the vouchers as billing for “direct” labor, i.e., hours of work whose expenditure directly accomplished the demands of the contract, rather than “indirect” labor. The government asserts that this labelling enabled Frost to recoup more money than he deserved by receiving additional payments for the fringe and overhead charges which accompany direct labor.

Before the trial, the government sent a letter to defense counsel which stated that the government would call a Chester Dailey as an expert witness to testify about the bonuses at issue. Dailey is a Contract Administrating Officer with the United States Defense Logistics Agency who oversaw the MDA contract between the Army and FWG during his employment.16 This letter stated in part:

> Please find enclosed the resume of Chester Daily. We presently plan to call him as a witness in connection with the MDA contract. He will authenticate documents and testify as to appropriate procurement procedures in connection with this contract. He will testify that in his opinion neither the contract itself nor government regulations allowed Dr. Frost to bill the government for bonuses disguised as direct labor. It is his opinion that this practice was deceptive. He bases this opinion on his experience in government and knowledge of the contract and regulations.

Counsel for Faulkner contacted Dailey both before and after receiving this letter, but Dailey, upon the advice of his agency’s counsel, declined to be interviewed. The government did not call Dailey as a witness. Although defendants initially had intended to call Dailey as a witness, they ultimately decided not to, due to the contents of the letter and his refusal to be interviewed.

After the trial, defendants learned that Dailey had told the government something other than precisely what the government had represented in its letter. Based upon this discovery, Frost filed a motion for a new trial or evidentiary hearing, arguing that the prosecution had failed to disclose exculpatory evidence provided by Dailey. In an affidavit attached to this motion, Dailey stated that he came to know Frost while overseeing the MDA contract, and that, contrary to the representations of the letter sent by the gov*382emment, he never had told anyone that he believed that Frost had billed the bonuses in a “deceptive” manner or had “disguised” them in any way. Further, Dailey stated that he did not meet with the prosecution until the trial was underway, and that he explained during this meeting that the bonuses may have been allowable as an indirect charge. Dailey also informed the prosecution that 1) he saw no evidence that Frost had billed the bonuses fraudulently or deceptively; 2) “FWG was a small business and small businesses often bill cost to the government in ways that they think are correct, but are technically disallowable;” and 3) if his agency had closed out the contract, the agency would have audited FWG and the contract, the auditor would have found that Frost had billed the bonuses as direct labor, and Frost knew that his agency would have audited the contract thoroughly.

The District Court denied the motion for a new trial or hearing. We will not reverse a refusal by a trial court to grant either a new trial or a hearing on a motion for new trial unless the court has abused its discretion. *See, e.g., United States v. O’Dell,*805 F.2d 637, 640, 643 (6th Cir.1986). A defendant requesting a new trial ordinarily must demonstrate the following:

> (1) the new evidence was discovered after trial;

> (2) the evidence could not have been discovered earlier with due diligence;

> (3) the evidence is material and not merely cumulative or impeaching; and

> (4) the evidence would likely produce an acquittal.

Id. at 640. However, when the defendant asserts that the new evidence at issue is exculpatory evidence which the government failed to turn over in violation of *Brady,*he “should not have to satisfy the severe burden of demonstrating that newly discovered evidence probably would have resulted in acquittal.” *Id.*at 641 (quoting *United States v. Agurs,*427 U.S. 97, 111, 96 S.Ct. 2392, 2401, 49 L.Ed.2d 342 (1976)). Rather, the defendant must show only that the favorable evidence at issue was “material,” with “materiality” defined according to opinions interpreting the *Brady*doctrine. *See id.; see also United States v. Schledwitz,*86 F.3d 73, 75 (6th Cir.)(Merritt, J., dissenting from denial of petition for rehearing *en banc*)(defendant faces different and more lenient standard if new trial motion rests on *Brady*claim), *cert. denied,*— U.S. —, 117 S.Ct. 357, 136 L.Ed.2d 249 (1996).

The Supreme Court recently has described in detail the analysis applicable to a *Brady*claim. *See Kyles v. Whitley,*514 U.S. 419, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995). The *Kyles*Court explained that *Brady,*373 U.S. at 87, 83 S.Ct. at 1196-97, requires the prosecution to provide evidence which is favorable to the accused and “material” to guilt or innocence, regardless of the good or bad faith of the prosecution. *See Kyles,*514 U.S. at 432, 115 S.Ct. at 1565. A *Brady*claim may arise when the government has introduced trial testimony which was known to be, or should have been recognized as, perjury; when the government has not honored a defense request for specific exculpatory evidence; or when the government has not volunteered exculpatory evidence not requested by the defense, or requested only generally. *See id.*at 433, 115 S.Ct. at 1565. Any favorable evidence, regardless of whether requested or not, is “material” if “there is a *reasonable probability*that, had the evidence been disclosed to the defense, the result of the proceeding would have been different.” *Id.*at 433-34, 115 S.Ct. at 1565 (quoting *United States v. Bagley,*473 U.S. 667, 682, 105 S.Ct. 3375, 3383-84, 87 L.Ed.2d 481 (1985))(emphasis added).17 Whether evidence is “material” does not depend upon “whether the defendant would more likely than not have received a different verdict *383with the evidence, but whether in its absence he received a fair trial, understood as a trial resulting in a verdict worthy of confidence.” *Id.*at 434, 115 S.Ct. at 1566. Accordingly, a *Brady*claim does not require a showing that introduction of the exculpatory evidence would have rendered the overall evidence insufficient to convict. *See id.*at 434-35, 115 S.Ct. at 1565-66.

The doctrine of harmless error does not apply once a court has found a *Brady*violation, because a *Brady*analysis necessarily includes a determination of whether the evidence at issue might have affected the verdict. *See id.*at 435, 115 S.Ct. at 1566. Finally, courts should evaluate the material effect of exculpatory evidence by examining the evidence collectively, not item-by-item. *See id.*at 436, 115 S.Ct. at 1566-67.

The District Court rejected the motion for new trial because it believed that Fed. R.Evid. 704(b) would have barred Dailey from testifying that Frost lacked the requisite intent to deceive. The District Court also found that Dailey could not have testified that small businesses like FWG often bill the federal government in ways which they believe are correct but which technically are not allowable because, “[i]n the absence of a proper foundation showing personal knowledge, Dailey would not be permitted to testify about his mere opinion as to the intent and motives of other government contractors and their billing practices.” Further, the District Court found that the proposed testimony that Frost knew that the billings at issue would be audited “does not necessarily prove that Frost lacked the requisite intent to defraud;” the District Court also stated that “[t]here is nothing in Dailey’s affidavit which indicates that he had personal knowledge of what Frost knew or was thinking on the subject of an audit.” Finally, the District Court stressed that the proposed testimony by Dailey favored the prosecution to the extent that it confirmed the basic claim that Frost could not have billed the bonuses as direct labor costs.18

We find that the District Court abused its discretion by not holding an evidentiary hearing on the motion for new trial. As noted, the court relied in part upon Federal Rule of Evidence 704(b), which states:

> (b) No expert witness testifying with respect to the mental state or condition of a defendant in a criminal case may state an opinion or inference as to whether the defendant did or did not have, the mental state or condition constituting an element of the crime charged or of a defense thereto. Such ultimate issues are matters for the trier of fact alone.

*See*Fed.R.Evid. 704(b). The District Court is correct that Rule 704(b) would bar Dailey from testifying that Frost lacked an intent to defraud. However, the affidavit by Dailey stated that there was no evidence that Frost billed the bonuses in a *deceptive manner.*Although it is unclear precisely what Dailey meant by this statement, he presumably was asserting that Frost used a billing method which made it obvious what he was doing. If so, this is a fact which would have allowed the jury to infer a lack of intent to defraud. Given the lack of strong evidence supporting the convictions, *see infra,*as well as the fact that Dailey would have been an effective defense witness as the government official who oversaw the MDA contract, the contract in issue, the District Court should have permitted an evidentiary hearing to develop Dailey’s testimony as to why the bonuses had not been billed in a “deceptive manner.”

Similarly, Rule 704(b) does not prohibit the proposed evidence that small businesses like FWG often bill costs in ways that they believe are correct but which technically are not allowable:

> Decisions applying Rule 704(b) to the expert testimony of law enforcement officials have found it significant whether the expert actually referred to the intent of the defendant or, instead, simply described in general terms the common practices of those who clearly do possess the requisite intent, leaving unstated the inference that *384the defendant, having been caught engaging in more or less the same practices, also possessed the requisite intent.

*United States v. Lipscomb,*14 F.3d 1236, 1239 (7th Cir.1994). In this case, Frost wishes to demonstrate the converse of the above principle by showing through expert testimony that he engaged in the same common practices of those who clearly lack the requisite criminal intent. Although the District Court questioned whether Dailey, whose job is to oversee government contracts, has personal knowledge of the motives and billing practices of contractors in general, his affidavit indicates that he has such knowledge. The proposed testimony that Frost knew that the government would audit the billings and discover that he had billed the bonuses as direct labor is yet another fact from which the jury could infer that Frost lacked an intent to defraud: generally, people are less inclined to lie if there is a likelihood that they will be caught.

We believe that Frost may be able to show a reasonable probability that the verdicts would have been different with Dailey’s testimony, and therefore show entitlement to a new trial on Counts Twenty-Five through Twenty-Nine. Crucial to our holding is the fact that the evidence supporting the convictions for these counts is not strong. Ultimately, the government relies upon three transcript pages of testimony by a government auditor who, after describing the difference between direct and indirect labor, answered “no” when the prosecution asked whether the government would have allowed Frost to “double his money” if Frost first had asked the government whether he could bill the bonuses as direct labor.

We do not hold that there is insufficient evidence to support a verdict of guilty. It remains unclear from the record, including the direct and cross-examination testimony of Frost and his experts, whether Frost in fact complied with regulations by establishing an informal bonus plan. Further, and after viewing the record in the light most favorable to the prosecution, there is substantial evidence which would allow a jury to infer that Frost had the intent to defraud the government. *See United States v.*DeCas*tris,*798 F.2d 261, 263 (7th Cir.1986)(affirming mail fraud convictions by observing that the concealment of “information known to be pertinent to a proper decision may be a fraudulent scheme,” even when the defendant could have shown that he in fact is entitled to a favorable decision). Nonetheless, the evidence of an intent to defraud is equivocal, and an evidentiary hearing may reveal a reasonable probability that the undisclosed testimony of Dailey would have resulted in different verdicts.

Frost and Turner vaguely suggest that the new testimony of Dailey requires a new trial or hearing for every count related to improper billing, including Counts Twenty-One through Twenty-Four. The new testimony, however, is related only to Counts Twenty-Five through Twenty-Nine, the counts based upon the billing of bonuses as direct costs. It is unrelated to Frost’s convictions of Counts Twenty-Three and Twenty-Four, which are based upon his billing the government for trips to Las Vegas and Reno, Nevada. Likewise, the testimony is unrelated to Frost’s and Turner’s convictions of Counts Twenty-One and Twenty-Two, which are based upon their billing the work of an FWG employee not according to which government contract he actually worked on, but according to which contract would enable Frost and Turner to request the most money. Although Potter moved to adopt the assertion by Frost on appeal that the undisclosed testimony by Dailey requires a new hearing or trial, the testimony of Dailey is similarly unrelated to any of the counts for which *Potter*stands convicted.

Faulkner appeals the denial of his motion for a new trial, which also was based on exculpatory evidence contained in the Dailey affidavit regarding the role of Faulkner in the extension of the MDA contract. We do not address this claim, however, because we already have vacated the convictions of Faulkner which rest upon his alleged act of modifying the MDA contract on behalf of Frost.

We further note that additional motions for new trials, which allege that the government suppressed an internal investigative report which concluded that FWG did not receive *385contract work from the student defendants in exchange for advanced degrees, remain pending before the District Court. We leave it to the District Court to dispose of these motions in light of this opinion.

B. False Declaration to Grand Jury

The jury convicted Congo of Count Thirty-One, which alleged that he violated 18 U.S.C. § 1623 by knowingly making a false material declaration when testifying before the grand jury that was investigating whether the schemes at issue in these prosecutions constituted mail fraud. The Superseding Indictment asserted that Congo testified as to the following before the grand jury:

> Q: Did you ever have — tell me what work did FWG employees do on your dissertation.

> A: Well, I’m not sure how you want me to answer that when you say what work did they do on my dissertation. The employees at FWG that offered to read over my dissertation and stuff were Jimmy Steele and Karen Seiser.

> Q: Did Karen offer to read over it?

> A: Yes.

> Q: That was her idea?

> A: Yes.

> Q: And Jimmy Steele’s idea to read over it?

> A: Yeah. I mean they knew I was working on it. And they said I’ll be glad to take a look at it. And, you know, specifically, what Jimmy did, there was what we call pull-down menus that Jimmy gave me, and I told this to Mr. Wilkes, there is a pull-down menu selection in my dissertation that Jimmy got his software from a Paradox training class that he took. I was talking to Jimmy one time about wanting to embellish my program, make it a little snazzier. And he said, here, try this. And so he gave me some program codes and it seemed to work well.

> Karen, I remember Karen offering to do these little fault-free boxes, if you will, in my dissertation, you know, where I draw the little boxes and I had them all drawn out, and I was going to try to figure out a way to take it over to the graphics department at Marshal and just let those guys do it. And she said I can do it, no sweat, I can do that, it won’t take me ten minutes. I said are you sure, and she said sure, no problem. Karen offered to do that.

> Q: How much time do you figure she spent on your dissertation?

> A: Karen?

> Q: Uh-huh.

> A: All in all maybe a week at the most. I think Karen started in the Huntsville office sometime around January or so of ’90, something along in there. And Jimmy on his thing I don’t know, ten hours, 15 hours, whatever.

> Q: Now, you say a week, would that mean a solid week at one time or—

> A: No.

> Q: —40 hours spread out over several—

> A: This was spread out over — well, let’s see. I first met Karen I think sometime around January and I more or less had everything all wrapped up in mid-February, so there is like a five, six-week time frame in there, so it’s sometime, 40 hours over five or six weeks.

> Q: You never heard anybody — were you ever aware of anybody ever complaining about having to work on your dissertation?

> A: Nobody ever worked on my dissertation, you know. I want to make that clear. Nobody worked on my dissertation. They offered to look at my dissertation as a colleague and a friend and such. I mean, when you’ve been working together for a long time, you really get to become colleagues. And Karen had just finished her dissertation the year before and I had used hers as the format for how to structure mine, so, no, I mean, they very willingly offered to look at it.

> *386Q: You say that these people worked on your dissertation as Mends, that’s the context in which you had them do it?

> A: I didn’t have them do it. They offered to do it.

Count Thirty-One alleged that the above testimony was false and in violation of § 1623 because Congo knew “that individual FWG employees did not offer to aid him in the preparation of his dissertation out of Mend-ship, but were directed to do so and did work on his dissertation because of his position with NASA.” The Superseding Indictment therefore did not base this count upon a claim that Congo lied about the amount of help which he received on his dissertation, but rather on a claim that he lied about the motives of those who helped him. The indictment further stated that “[i]t was material to the investigation that the grand jury ascertain whether [Congo] had abused or misused his position as COTR on a contract between NASA and FWG Associates, Inc.”

Congo asserts that his § 1623 conviction cannot stand because there is insufficient evidence that he lied to the grand jury. Specifically, he argues that his statements that Karen Seiser and Jimmy Steele offered to work on his dissertation as colleagues and Mends are literally true. The falsity of the statements at issue is necessarily an element under § 1623. *See, e.g.,*18 U.S.C. § 1623; *United States v. Gulley,*992 F.2d 108, 112 (7th Cir.1993).

Congo is correct that the government failed to introduce any evidence regarding the motives of Jimmy Steele. He also is correct that Seiser, who consistently testified that she worked on his dissertation only because Turner had instructed her to, testified during cross-examination that it probably was she who approached Congo regarding her working on his thesis, and that she never explicitly informed him while working on the thesis that she was acting only according to the instructions of Turner. Nonetheless, Seiser also testified that, during a lunch initiated by Congo in the summer of 1990, before the grand jury proceedings but during the investigation by the government, Congo stated to Seiser that he saw her help in writing his dissertation as though she was helping him out as a personal Mend and colleague. Seiser testified, however, that she responded to Congo by explaining that “I didn’t necessarily see it that way, that I was being paid by FWG, and I didn’t, I didn’t necessarily do it as a Mend, I did it as a paid employee.” This testimony provides sufficient support for the conclusion by the jury that Congo lied when he claimed that he believed that FWG employees offered to work on his thesis out of Mendship.

Moreover, the record contains circumstantial evidence that Congo knew that his statement that Seiser had offered to work on his dissertation as a colleague and a Mend was false, including evidence that 1) Seiser perhaps had met Congo for thirty seconds before working at FWG and was not a Mend of his; 2) Seiser began working on his dissertation shortly after she began to work at FWG; 3) Congo ordered Seiser about as if she were an employee; 4) Congo wrote a memo to the secretary of Frost in which he directed the secretary “to have Karen Siser [sic] redo table 18;” and 5) Congo admitted that he thought that Seiser had spent the equivalent of a full work week on his dissertation, a significant sacrifice for one motivated solely by Mendship and eollegiality. Sufficient evidence therefore supports the finding that Congo lied about his beliefs concerning the motives of Seiser.

Congo also argues that his § 1623 conviction must be reversed because the District Court, rather than the jury, decided the issue of whether his false statements to the grand jury were “material.” Materiality is an element of perjury under § 1623. *See Johnson v. United States*, — U.S. -, -, 117 S.Ct. 1544, 1548, 137 L.Ed.2d 718 (1997). Further, the jury, not the court, must decide the issue of materiality under § 1623. *See id.; see also United States v. Gaudin,*515 U.S. 506, 115 S.Ct. 2310, 132 L.Ed.2d 444 (1995)(assuming 18 U.S.C. § 1001 has materiality element, jury must decide issue). When a defendant did not object to the trial court deciding materiality, we apply Federal Rule of Criminal Procedure 52(b), which provides that “[p]lain errors or defects affecting substantial rights may be noticed although they were not *387brought to the attention of the court,” in order to decide whether we should correct the error. *See Johnson,*— U.S. at-- -, 117 S.Ct. at 1548-49.

Congo concedes that he did not object when the District Court decided the materiality of his statements. He nonetheless insists that the failure of the District Court to allow the jury to decide materiality necessarily requires reversal because such an error is “structural.” The *Johnson*Court, however, explicitly rejected this argument and held that Rule 52(b) applies when a defendant during a direct criminal appeal did not object before the trial court, regardless of whether the error claimed is structural. *See id.*at -, 117 S.Ct. at 1548; *see also United States v. Sassanelli,*118 F.3d 495, 499 (6th Cir.1997)(under *Johnson,*Rule 52(b) applies to structural errors).

Before an appellate court may correct an error not raised at trial, the defendant must satisfy a four-part test imposed by Rule 52(b). He must demonstrate that “(1) that the instruction was error; (2) that the error was plain; (3) that the plain error affected the defendant’s substantial rights; and (4) that the court should exercise its discretion to correct the error because the error ‘seriously affected the fairness, integrity, or public reputation of judicial proceedings.’ ” *Sassanelli,*118 F.3d at 499 (quoting *Olano,*507 U.S. at 732, 113 S.Ct. at 1776-77).

In this case, the failure of the District Court to submit the issue of materiality to the jury was “error.” *See Johnson,*— U.S. at — , 117 S.Ct. at 1549.19 Further, the error was “plain,” because the law at the time of trial, which held that materiality was a question of law, *see, e.g., United States v. Adams,*870 F.2d 1140, 1147 (6th Cir.1989), was both settled and clearly contrary to current law. *See Johnson,*— U.S. at-, 117 S.Ct. at 1549. Accordingly, Congo has satisfied the first two elements of the four-part test under Rule 52(b).

Congo, however, cannot satisfy the fourth requirement, that the error “seriously affected the fairness, integrity or public reputation of judicial proceedings.” In *Johnson,*the defendant was unable to satisfy this final requirement because the evidence of materiality was “overwhelming;” the Court found that the defendant “presented no plausible argument” that her lying about the source of tens of thousands of dollars which she had used to improve her home was not material to the grand jury investigation, which in part concerned whether the defendant’s boyfriend had concealed his drug proceeds as real estate investments. *See id.*at-, 117 S.Ct. at 1550. Likewise, we believe that the evidence of materiality in this case was overwhelming. A statement is material under § 1623 “if it has ‘a natural tendency to influence, or be capable of influencing, the decision of the decisionmaking body to which it is addressed.’” *Sassanelli,*118 F.3d at 499 (quoting *Gaudin,*515 U.S. at 509, 115 S.Ct. at 2313 (quoting *Kungys v. United States,*485 U.S. 759, 770, 108 S.Ct. 1537, 1546, 99 L.Ed.2d 839 (1988))); *see also United States v. Rogers,*118 F.3d 466, 470 (6th Cir.1997)(artieulating identical test for materiality of statement under 18 U.S.C. § 1001). Although a false statement must have the *capacity*to influence a decision, it does not have to be actually influential in order to be material. *See Rogers,*118 F.3d at 472. In this case, the grand jury was investigating whether Frost and Turner were helping students to attain their degrees without completing legitimate dissertations in exchange for agreements by the students to use their government positions to secure contracts or contract modifications for FWG. Whether the FWG employees who worked on the thesis of Congo did so voluntarily and on the basis of friendship, or instead acted out of compulsion and at the direction of Frost, is a question whose resolution was clearly capable of influencing the grand jury in its determination of whether defendants were participating in a fraudulent degrees-for-contracts scheme. *See Sassanelli,*118 F.3d at 499, 500 (because there was “no serious argument” that denial by defendant of any involvement in false invoice scheme at issue could not have influenced court presiding over civil action *388against defendant, defendant-failed to satisfy fourth prong of Rule 52(b) test); *United States v. McGhee,*119 F.3d 422, 424 (6th Cir.1997)(fourth prong of Rule 52(b) test not satisfied when evidence of materiality was overwhelming); *see also Rogers,*118 F.3d at 472 (failure to submit materiality to jury did not “affect substantial rights” under third prong of Rule 52(b) test when lie was capable of influencing FBI agents even though agents knew its falsity); *United States v. Barrow,*118 F.3d 482, 493 (6th Cir.l997)(because evidence established unquestionable materiality of false statements to IRS regarding income, impossible for defendant to satisfy fourth prong of Rule 52(b)). Indeed, like the defendants in *Johnson,*— U.S. at -, 117 S.Ct. at 1550, *Sassanelli,*118 F.3d at 499, and *McGhee,*119 F.3d at 424, Congo has not challenged the materiality of the lie for which the jury convicted him, although he has challenged the sufficiency of the evidence that he lied.20 Rather, he has argued only that not instructing the jury on materiality requires reversal because it is a structural error, a claim foreclosed by *Johnson.*

This conclusion does not contradict our prior finding that insufficient evidence supports the mail fraud convictions of Congo based upon the degrees-for-contracts theory. *See supra*Section II.A. “[Materially false grand jury testimony is a criminal offense, regardless of whether the grand jury’s investigation ultimately leads to a valid indictment for a federal offense.” *Callanan v. United States, 881*F.2d 229, 236 (6th Cir.1989)(upholding § 1623 conviction for perjury concerning mail fraud scheme, even though later convictions for mail fraud scheme were vacated because they were based upon intangible rights to honest services doctrine invalidated by *McNally).*Accordingly, the fact that the government has failed to prove that Congo committed mail fraud by abusing his government position on behalf of Frost and Turner does not prevent his misstatement regarding the motives of the FWG employees who worked on his thesis from being perjury.

C. Suppression of Seized Evidence

Frost asserts that all of the evidence seized by the federal agents who searched the offices of FWG pursuant to a search warrant must be suppressed. He argues that probable cause did not support the warrant, that the warrant was overly broad, and that the agents flagrantly disregarded the scope of the warrant when conducting the search. Frost relies mainly upon his pleadings filed below, and the government relies exclusively upon the order and memorandum of the District Court refusing to suppress all evidence, but reserving until trial the issue of whether particular documents sought to be introduced should be suppressed.

Having reviewed the pleadings and exhibits filed by Frost, including the search warrant and its supporting affidavit, as well as the rulings of the District Court, we find no error. Frost relies primarily upon *United States v. Medlin,*842 F.2d 1194, 1199 (10th Cir.1988), in which the Tenth Circuit suppressed all seized evidence when an officer acted in flagrant disregard of the terms of the search warrant. The agent in *Medlin,*however, seized 667 items other than firearms, even though the warrant authorized the seizure of firearms *only. See id.*at 1195-96. In this case, the agents did not “flagrantly” exceed the scope of the warrant, which appropriately authorized the extensive seizure of paper and computer documents in this complicated mail fraud case. See *United States v. Henson,*848 F.2d 1374, 1383-84 (6th Cir.1988).

D. Motions to Sever

Potter and Frost claim that the District Court erred by not granting their motions to sever. Although the arguments raised by Frost are very brief, he appears not to contest the joinder of his case with those of the other defendants, but argues only that not every count should have been joined against him. Potter primarily argues *389that her ease should not have been joined with those of her eodefendants, although she also asserts that the counts against her were joined improperly.

Defendants argue that this case should have been tried as several cases, with separate prosecutions for Counts 1) One through Sixteen; 2) Seventeen through Twenty; 3) Twenty-One through Twenty-Nine; 4) Thirty; and 5) Thirty-One. They suggest that we should apply Federal Rule of Criminal Procedure 8(a), rather than Rule 8(b), when deciding the precise question of whether the indictment properly combined all counts into a single prosecution.

Rule 8 requires a trial court to examine the allegations of the indictment in order to determine whether the joining of the offenses and/or defendants has been proper. *See, e.g., United States v. Lloyd,*10 F.3d 1197, 1214 (6th Cir.1993); *United States v. Holloway,*971 F.2d 675, 679 (11th Cir.1992). Rule 8 provides:

> Rule 8. Joinder of Offenses and of Defendants

> (a) Joinder of Offenses. Two or more offenses may be charged in the same indictment or information in a separate count for each offense if the offenses charged, whether felonies or misdemeanors or both, are of the same or similar character or are based on the same act or transaction or on two or more acts or transactions connected together or constituting parts of a common scheme or plan.

> (b) Joinder of Defendants. Two or more defendants may be charged in the same indictment or information if they are alleged to have participated in the same act or transaction or in the same series of acts or transactions constituting an offense or offenses. Such defendants may be charged in one or more counts together or separately and all of the defendants need not be charged in each count.

Fed.R.Crim.P. 8.

Traditionally, courts have held that Rule 8(a) applies only to a prosecution of a single defendant, and that Rule 8(b) applies exclusively whenever multiple defendants are involved, even if a defendant is contesting only the joinder of counts against himself. *See*1 Charles Alan Wright, Federal Practice and Procedure: Federal Rules of Criminal Procedure § 143 p. 479, § 144 p. 494 (2d ed.1982). The primary difference between the two sections is that it is easier to justify joinder under Rule 8(a) because, unlike Rule 8(b), it also permits joinder of offenses which are merely of “the same or similar character.” *See id.*at § 144 pp. 495; *see also United States v. Eufrasio,*935 F.2d 553, 570 n. 20 (3d Cir.1991). One court, however, has held that Rule 8(a) applies where, unlike this case, all the defendants were charged with and tried on the same counts. *United States v. Southwest Bus Sales, Inc.,*20 F.3d 1449, 1454 (8th Cir.1994). Further, another court has suggested that, contrary to the traditional rule, the more lenient Rule 8(a) applies when a defendant in a multiple-defendant prosecution challenges only the joinder of the offenses charged against himself. *See Eufrasio,*935 F.2d at 570 n. 20. Rule 8(a) therefore may apply in this case to the joinder of the counts against Frost.

Like the *Eufrasio*court, however, we ultimately will not decide whether Rule 8(a) has any application in this ease, *see id.*at 570, because reversal is not warranted even under Rule 8(b).

“The joinder of multiple defendants is proper under Rule 8(b) only if each of the counts of the indictment arises out of the same act or transaction or series of acts or transactions, even if all counts of the indictment include a common defendant.” *Lloyd,*10 F.3d at 1215 (quoting *United States v. Hatcher,*680 F.2d 438, 441 (6th Cir.1982)). “[A] group of acts or transactions constitutes a ‘series’ if they are logically interrelated.” *Id.*(quoting *United States v. Johnson,*763 F.2d 773, 777 (6th Cir.1985)).

Although the question of whether joinder was proper under Rule 8(b) is a question of law, *see, e.g., Hatcher,*680 F.2d at 441, misjoinder does not require reversal per se. Rather, we review for harmless error, and will reverse only if joinder has “resulted] in ‘actual prejudice’ because it had a ‘substantial and injurious effect or influence’ on the jury’s verdict.” *Lloyd,*10 F.3d at *3901214 (quoting *United States v. Lane,*474 U.S. 438, 449, 106 S.Ct. 725, 732, 88 L.Ed.2d 814 (1986)).

The District Court denied defendants’ motions to sever because it found that every allegation related to an overall scheme to enrich Frost and FWG by defrauding the government, and that every charge concerned various, and sometimes identical, contracts between FWG and NASA or the Department of Defense. The District Court also stated that there was substantial overlap of proof, and that the actions underlying Counts One through Twenty-Nine all occurred during the same period of time. Finally, the District Court found that Counts Thirty and Thirty-One directly related to the other counts because the mail fraud charged in the preceding counts motivated the attempts to cover up the alleged mail fraud.

The joining of Counts One through Twenty, as well as Counts Thirty and Thirty-One, was proper. Counts One through Twenty all concerned an alleged uniform scheme to defraud the government and the University of Tennessee out of either money or degrees, and the collective effort to fabricate a plagiarized dissertation or thesis was integral to every count. As we have observed, the “predominant consideration” of a decision regarding joinder under Rule 8(b) is “whether joinder would serve the goals of trial economy and convenience; the primary purpose of this kind of joinder is to insure that a given transaction need only be proved once.” *United States v. Moreno,*933 F.2d 362, 369 (6th Cir.1991)(quoting *United States v. Swift,*809 F.2d 320, 322 (6th Cir.1987)(quoting *United States v. Franks,*511 F.2d 25, 29 (6th Cir.1975))); *see also United States v. Stillo,*57 F.3d 553, 556-57 (7th Cir.)(policy of liberal joinder enhances judicial efficiency and allows jury to hear “total story”), *cert. denied,*— U.S.-, 116 S.Ct. 383, 133 L.Ed.2d 306 (1995). Severing either the defendants or the counts as they relate to the allegations of academic impropriety would have required the government to prove repeatedly the same series of transactions. Further, and as the District Court pointed out, Rule 8(b) allows joinder of counts based on attempts to cover-up guilt for charged counts. *See United States v. Curry,*977 F.2d 1042, 1049-50 (7th Cir.1992)(perjury); *United States v. Carmichael,*685 F.2d 903, 909-10 (4th Cir.1982)(obstruetion of justice).

Depending upon how broadly one defines “the same series of acts or transactions” under Rule 8(b), the District Court also may have been correct that Counts Twenty-One through Twenty-Nine, which concerned fraudulent billing of the government under FWG contracts, were joined properly with the remaining counts. Even if these counts were misjoined, however, any possible error was harmless. *See, e.g., Holloway,*971 F.2d at 679 (declining to decide whether joinder was improper under Rule 8(b) when any error was harmless). The only defendant who has identified on appeal any specific prejudice arising from the joinder of these counts is Potter, and even she confines herself to noting that the government introduced evidence that Frost lived an “extravagant lifestyle,” improperly billed time, sought improper expense reimbursements, tried to destroy evidence, and generally had bad character. She also complains that one witness alleged that Turner offered to give exam questions to the parent of a student.

We initially note that the evidence of Frost’s “extravagant lifestyle” and Turner’s invitation to cheat was applicable to Counts One through Twenty, for which joinder was clearly proper.21 Moreover, the evidence that Frost tried to destroy evidence presumably did not impress the jury significantly because it acquitted Frost of that count. Most importantly, however, the convictions of Frost and Potter which have withstood our review all rest upon overwhelming evidence. As we already have explained, *see supra*Sections II.B and C, the record easily yields the conclusion that each defendant participated in a secret scheme in which the student *391defendants received their graduate degrees without having completed a legitimate thesis or dissertation, thereby defrauding the University of the honest services of Frost and Turner and the government of tuition money. Further, Frost has not challenged the evidence under Counts Twenty-One to Twenty-Four proving that he fraudulently billed the government. *See United States v. Randazzo,*80 F.3d 623, 628 (1st Cir.1996)(although joinder was improper under Rule 8(a), error was harmless because evidence was overwhelming); *United States v. Epley,*52 F.3d 571, 578 (6th Cir.1995)(even if joinder was improper under Rule 8(b), ample evidence showed that error was harmless).

The District Court further minimized any prejudice by instructing the jury to consider only the evidence against each defendant on each charge, and to return separate verdicts, without regard to the other charges or defendants. *See Southwest Bus Sales,*20 F.3d at 1454 (even if joinder was improper, error was harmless partly due to limiting instructions); *Stillo,*57 F.3d at 557 (under Fed.R.Crim.P. 14, instructions to consider evidence only in relation to person against whom it was admitted reduces risk of prejudice). Although Potter insists that the fraudulent billing counts are unrelated to the academic impropriety counts, she thereby also highlights the fact that it would not have been difficult for the jury to compartmentalize and distinguish the evidence concerning the allegedly different schemes. *See United States v. Elder,*90 F.3d 1110, 1119-20 (6th Cir.1996)(fact that evidence concerning defendant was easy to compartmentalize and separate from evidence against other defendants showed lack of prejudice under Rule 14), *cert. denied,*— U.S. -, 117 S.Ct. 993, 136 L.Ed.2d 873 (1997); *Stillo,*57 F.3d at 557 (holding the same). Similarly, the evidence and arguments at trial mainly focused on Counts One through Twenty, the heart of the prosecution, thereby minirnizing any distracting and prejudicial effects of the allegedly misjoined counts. *United States v. Bibby,*752 F.2d 1116, 1122 (6th Cir.1985)(misjoinder harmless in part due to relatively minor role of misjoined counts).

We therefore find that any initial misjoinder under Rule 8(b) did not result in “actual prejudice” by exerting a “substantial and injurious effect or influence” on the verdicts. Potter also has invoked Federal Rule of Criminal Procedure 14, which “comes into play only if joinder was initially proper under Rule 8 but a joint trial would prejudice one or more defendants.” *Lloyd,*10 F.3d at 1215. We review a denial of severance under Rule 14 for abuse of discretion only. *See id.*Because we already have examined the potential sources of prejudice when deciding whether any misjoinder under Rule 8(b) was harmless, we find that, at least under the circumstances of this case, the Rule 14 claim necessarily fails.

E. Sentencing Issues

■ Because we have vacated some convictions for every defendant, we remand in order for the District Court to review each sentence in light of the vacated counts. We will address briefly two particular arguments raised by Potter and Frost regarding their sentences because these issues will arise on resentencing.

Frost claims that the District Court erred when calculating the loss attributable to the scheme to bill bonuses as direct expenses by including in the amount of loss the full value of the bonuses, in addition to the overhead costs attributable to the bonuses having been identified as direct, not indirect, expenses. We note only that, if the District Court determines that the convictions based upon the bonus billing scheme should not be reversed because of a *Brady*violation, *see supra*Section IV.A, the District Court should make a specific factual finding at sentencing as to whether Frost and FWG had an informal bonus plan in existence that would have allowed the payment of some form of bonuses.

Potter claims that the District Court erred when calculating the loss attributable under Count Eight, which charged her with defrauding the government of her tuition money. We review the factual findings underlying a sentencing decision for clear error. *See, e.g., United States v. Hill,*79 F.3d 1477, 1481 (6th Cir.), *cert. denied,*— U.S. -, 117 S.Ct. 158, 136 L.Ed.2d 102*392(1996). The District Court found that Potter had defrauded the government of $2159, the full amount of the UTSI invoice at issue. Because the loss caused by the offense was over $2000, the District Court enhanced her sentence by one point under United States Sentencing Guideline § 2Fl.l(b)(l)(B).

Potter complains that NASA lost only about $750 because she educated herself by working hard to understand the FWG report which she would pass off as her thesis, and because she did not engage in the fraudulent scheme at issue until her last semester, when she submitted her thesis. It was not clearly erroneous, however, for the District Court to find that NASA was not paying for Potter to gain some minimal understanding of a topic in order to pass her oral defense, but to get a degree based upon a legitimate thesis.

V. Conclusion

Accordingly, we VACATE the convictions of each defendant convicted of Counts Two through Seven, Nine through Fourteen, and Sixteen. We AFFIRM the convictions of each defendant convicted of Counts One, Eight, Fifteen, Seventeen, and Nineteen through Twenty-Four, as well as the conviction of Congo of Count Thirty-One. We REMAND for a hearing as to whether Frost should receive a new trial for his convictions of Counts Twenty-Five through Twenty-Nine on the basis of a *Brady*violation. Finally, we REMAND all sentences for review in light of this opinion, but AFFIRM the valuation by the District Court of the loss caused by the offense of which Potter was convicted under Count Eight.

1

. If the prosecution now is relying upon an alleged attempt on March 16, 1990 to recommend an extension of the MDA contract, we question whether the mailings at issue can support the convictions. The most recent mailing, a voucher dated March 15, 1990, pertained to work previ*357ously performed under the original MDA contract. How this mailing furthered a scheme to extend the length of the contract beyond .its original deadline of July, 1990 is unclear.

2

. Although Congo stresses that some NASA officials knew that he was acting as the COTR for a contract with a company headed by his major professor, there is no evidence that any NASA officials knew that he had agreed to help Frost obtain the chemical hazards contract in return for a dissertation.

3

. The *Mittelstaedt*Court made it clear that it was not reviewing convictions for depriving another of the intangible right to honest services under § 1346. *See id.*at 1216.

4

. Accordingly, Count Seventeen was based upon the November 8, 1989 certification for Potter; Count Eighteen was based upon the January 22, 1990 certification for Hill; Count Nineteen was based upon the March 26, 1990 certification for Congo; and Count Twenty was based upon the March 27, 1990 certification for Faulkner.

5

. Whether defendants’ mere status as employees of a state university would qualify them as public or quasi-public officials is unclear. *But see United States v. ReBrook III,*837 F.Supp. 162, 171 (S.D.W.Va.1993)(under mail fraud act, *any*state employee owes fiduciary duty to public to provide honest services), *off d in part, rev’d in part on other grounds,*58 F.3d 961 (4th Cir.1995).

6

. Opinions which condition an honest services conviction upon a "material” misstatement or omission often imply that only a deception which threatens the economic interests of the victim may qualify as "material.” For example, in *Cochran,*an underwriter misrepresented to the intended victim that it had not received a fee from a third-party which, due to the efforts of the underwriter, had entered into a contract with the intended victim. *See Cochran,*109 F.3d at 667-68. The *Cochran*court held that this misrepresentation could not support an honest services prosecution under the wire fraud act because it "resulted in no actual or potential harm" to the alleged victim, and because there was no evidence that the victim would have acted differently if it had known the truth. *See id.*at 669. Similarly, the *Jain*court ruled that a psychologist who had failed to disclose to his patients the fact that he was receiving unethical referral fees from an interested third-party mental health care provider did not intend to defraud his patients because "[t]here is simply no evidence that any patient would have considered Dr. Jain’s relationship with [the third-party] material if it did not affect the quality or cost of his services to that patient.” *Jain,*93 F.3d at 442.

7

. *See, e.g., United States v. Conner,*752 F.2d 566, 574 (11th Cir.1985)(wire and mail fraud); *United States v. Bohonus,*628 F.2d 1167, 1173-74 (9th Cir.1980); *United States v. Collins,*596 F.2d 166, 168 (6th Cir.1979); *United States v. Feinberg,*535 F.2d 1004, 1010 (7th Cir.1976). Other cases have rejected vagueness claims by examining the conduct of the defendants at issue but without explicitly noting whether the challenges were facial or as applied. *See, e.g., United States v. Stewart,*872 F.2d 957, 959 (10th Cir.1989); *United States v. Condolon,*600 F.2d 7, 9 (4th Cir. 1979); *United States v. Louderman,*576 F.2d 1383, 1388 (9th Cir.1978).

8

. Congo has labelled this argument as a claim that the mail fraud statute is unconstitutionally vague "as applied.” The claim actually asserted, however, rests solely upon the instructions rendered in this case, and does not refer to factual circumstances.

9

. The only indication in the record of an objection to this sentence is a general objection Hied by Frost on April 21, 1995. We nonetheless have assumed that defendants have preserved the instant argument.

10

. Further, the assertion by Potter that she did not participate in the mailings or "induce" anyone to use the mails does not constitute a defense to mail fraud. *See Oldfield,*859 F.2d at 400.

11

. Specifically, the District Court stated the following:

> All right. Members of the jury, we got your message here, and so I want to give you a further instruction in this case. We're going to ask that you return to the jury room and deliberate further. And I’m talking about the message that indicated that you were unable to agree on certain counts and certain matters. And I realize that you are having some difficulty in reaching unanimous agreement, but that is not unusual. And sometimes after further discussion, jurors are able to work out their differences and to agree.

> Please keep in mind how very important it is for you to reach unanimous agreement. If you cannot agree, and if this case is tried again, there is no reason to believe that any new evidence will be presented, or that the next 12 jurors will be any more conscientious and impartial than you are.

> Now, let me remind you that it is your duty as jurors to talk with each other about the case, to listen carefully and respectfully to each other’s views, and to keep an open mind as you listen to what your fellow jurors have to say. And let me remind you that it is your duty to make every reasonable effort you can to reach unanimous agreement. Each of you, whether you are in the majority or the minority, ought to seriously reconsider your position in light of the fact that other jurors, who are just as conscientious and impartial as you are, have come to a different conclusion.

> Those of you who believe that the government has proved the defendant guilty beyond a reasonable doubt should stop and ask yourselves if the evidence is really convincing enough, given that other members of the jury are not convinced. And those of you who believe that the government has not proven the defendant guilty beyond a reasonable doubt should slop and ask yourselves if the doubt you have is a reasonable one, given that other members of the jury do not share your doubt. None of you should hesitate to change your mind if, after reconsidering things, you are convinced that the other jurors are right and that your original position was wrong.

> But remember this. Do not ever change your mind just because other jurors see things differently, or just to get the case over with. As I told you before, in the end, your vote must be exactly that — your own vote. As important as it is for you to reach unanimous agreement, it is just as important that you do so honestly and in good conscience.

> What I have just said is not meant to rush or pressure you into agreeing on a verdict. Take as much time as you need to discuss things. There is no hurry.

> I would ask that you now return to the jury room to resume your deliberations.

12

. The particular response of the *Lash*court to the note is significant. Arguing that the note revealed juror frustration at the difficulty of reaching a verdict, a defendant in *Lash*cited *United States v. Foster,*711 F.2d 871 (9th Cir.1983), which upheld an *Allen*charge in part *376because juror notes in that case asking to be excused did not express such frustration. The *Lash*court rejected the claim that evidence of juror frustration required reversal, explaining that defendant "seeks to deduce from [Foster] the logical opposite, that mistrial is required when such a frustration occurs. Logic does not yield such an inference.” *Id.*

The *Lash*opinion illustrates how a trial court does not abuse its discretion merely because the case presents some indicia of coercion greater than cases in which an *Allen*charge was upheld.

13

. As noted, the jury returned its verdicts about two hours after having received the *Allen*charge. The amount of time spent deliberating after having received an *Allen*charge cannot be a factor indicating coercion, *see Tines,*70 F.3d at 896, although it can show whether a coercive charge was harmless. *See Williams,*741 F.2d at 850 n. 2; *United States v. Giacalone,*588 F.2d 1158, 1168 (6th Cir.1978); *cf. Scott,*547 F.2d at 337 (fact that jury agreed fourteen minutes after receiving coercive charge illustrated prejudicial impact of charge). Because the charge in this case was not coercive, however, we do not address the issue of harmlessness.

14

. It is unclear when Shelby left the jury room. Defendants assert that Shelby left around 4:00 p.m., after the reading of the *Allen*charge. In its memorandum denying the motions for new trials or a hearing, however, the District Court stated that Shelby left around 2:00 p.m., before the *Allen*charge. Both of these asserted times are somewhat suspect: because Shelby was absent from the juiy room for about twenty minutes, she likely could not have been present when the District Court delivered the *Allen*charge at 2:15 p.m. if she had left at 2:00 p.m.; alternatively, Shelby likely could not have been present when the jury delivered its verdicts at 4:15 p.m. if she had left at 4:00 p.m. Further, the District Court never had any knowledge of her absence, and defendants have relied only upon allegations in their briefs during these appeals.

15

. We likewise decline to determine whether the proper standard of review for a claim of implied bias is *de novo, see Hunley,*975 F.2d at 318-19, or whether the issue presents a mixed question of law and fact. *See Cummings v. Dugger,*862 F.2d 1504, 1509 (11th Cir.1989). Our holding is the same under either standard.

16

. The MDA contract was the largest contract which FWG had and was the principal source of the bonuses.

17

. A more defense-friendly standard of "materiality” applies when the prosecutor has relied upon perjured testimony: the defendant only must show that ("there is [a] reasonable likelihood that the false testimony could have affected the judgment of the jury.” *O’Dell,*805 F.2d at 641 (quoting *Bagley,*473 U.S. at 678, 105 S.Ct. at 3381)). Frost argues that we should apply this standard to this case. The prosecution, however, simply did not introduce perjured testimony at trial. Even under the more traditional "materiality” standard, however, a hearing is required on the *Brady*claim. *See infra.*

18

. The parties therefore dispute only whether the evidence at issue was "material,” not whether it was discovered after trial or whether defendants could have discovered it earlier through due diligence. Regardless, the record indicates that defendants did not discover the evidence until after trial, and that defense counsel employed due diligence by attempting to interview Dailey.

19

. The legal rule rendering this failure "error” applies retroactively to this case, because the Supreme Court announced the rule while this direct appeal still was pending. *See id.*

20

. In his appellate brief, Congo does preface one facet of his structural-error argument by stating, "Even if the evidence was overwhelming in support of the claim that Richard Congo's statements were material to the grand jury’s finding, which it is not,.... ” We do not believe that this statement sufficiently articulates why the evidence of materiality is not overwhelming.

21

. Further, we have upheld a refusal to grant a motion to sever despite the claim by a defendant that she suffered severe prejudice partly because the government introduced evidence concerning a codefendant's wealth and expenditures on luxury items. *See United States v. Warner,*971 F.2d 1189, 1196 (6th Cir.1992).