Jim Guy Tucker, the Governor of Arkansas until his conviction in this ease, appeals from his conviction for conspiracy and mail fraud. Tucker was indicted in a twenty-one count indictment, together with James and Susan McDougal, the former controlling persons of Madison Guaranty Savings and Loan, a thrift institution that failed. The first count of the indictment charged an overarching conspiracy to misuse the funds of Madison and of Capital Management Services, a small business investment company headed by alleged co-conspirator and key government witness David Hale. Tucker was indicted on the conspiracy charge and ten substantive counts based on individual transactions. At the close of the government’s case, the district court dismissed Counts 8-11.1 The remainder of the case was submitted to the jury, which acquitted Tucker of Counts 2-4 and 20-212 and convicted him of Count 1, conspiracy, 18 U.S.C § 371 (1994), and Count 12, mail fraud in connection with a loan from Capital Management Services to Castle Sewer and Water Corp. 18 U.S.C. § 1341 (1994).
On appeal, Tucker contends the convictions should be reversed because after trial it was discovered that a juror was married to a former state prisoner to whom Tucker, as governor, had denied clemency. Tucker also attempted to establish that the juror and her husband had engaged in discussions about the ease during the trial. Tucker further objected to the empaneling of a juror who gave answers to a written jury questionnaire that were inconsistent with a defendant’s right to remain silent and the presumption of innocence. Tucker contends that there was insufficient evidence to convict him of mail fraud and conspiracy. He also raises several points of evidentiary and instructional error. We conclude that Tucker has not demonstrated error on any ground except for the limitations the district court imposed on the hearing concerning alleged misconduct of one juror. We remand for a fuller hearing on the issues pertaining to the one juror.
The government’s case involved the several mutually dependent business transactions of Jim Guy Tucker, Susan and James McDougal, and David Hale, as described in *1020the testimony of David Hale. Hale was a municipal judge in Little Rock, where the McDougals operated Madison Guaranty and where Tucker practiced law. All were active in state politics in one capacity or another and all had multifarious business interests.
Hale described a meeting between Tucker, James MeDougal, and himself in the fall of 1985. The three 'went out to a new development called Castle Grande, which MeDougal had developed, to view thirty-four acres of property MeDougal had just sold Tucker. In fact, MeDougal had made Tucker buy the property as a prerequisite to Madison loaning Tucker money he needed to pay off another debt. After viewing the thirty-four acres, the three went to Tucker’s house and sat around the kitchen table, visiting. James MeDougal asked Hale about the lending limit of Capital Management Services, Hale’s small business investment company. Hale told MeDougal that the lending limit was $150,000.
The lending limit was a function of the amount of capital Hale had available to invest in Capital Management Services. The owner of a small business investment company would invest a certain amount, and the Small Business Administration would then provide three times the amount of that capital for the company to lend to small businesses. The company could only lend a particular borrower an amount equal to thirty percent of the company’s capital. Since Hale had $500,000 capital in the company at that point, his lending limit to a particular borrower was therefore $150,000.
After asking Hale about his lending limit, James MeDougal then turned to Tucker and said, “We’re going to have to get some more money into David’s SBIC [small business investment company].” MeDougal said, “I’m going to need some funds, and Jim Guy is going to need some funds, and we’re going to have to clean up—clean up some members of the political family____” The three decided that Hale should sell some property to generate the capital needed to increase Capital Management’s lending limit to $300,000, so it could make loans for the benefit of Tucker and MeDougal. They settled on a piece of property used for a restaurant known as Etta’s Place. The three .discussed whether the Etta’s Place property would appraise out at a high enough value to generate a profit of $500,000, but MeDougal said to let him worry about that. ' They agreed Hale should sell this property to a straw man to generate a profit of $500,000. Madison would loan the purchase money to the straw man. Hale would then invest the money in Capital Management Services. For every dollar Hale invested in Capital Management, the Small Business Administration would make available three dollars for Capital Management to loan to other businesses. In this way, the friends could leverage a dollar lent by Madison to the straw man into four dollars of available money.
In order to get an appraisal to support the Etta’s Place deal, Hale’s colleague, William Watt, hired Robert Palmer to appraise the property. Upon first looking at the property, Palmer reported to Watt that it would only be worth $300-400,000. Watt told him that the appraisal was for David Hale, who was “doing a favor” for James MeDougal, and that Hale needed an appraisal of $750,-000. Watt told Palmer to “do whatever you have to do.” Palmer issued an appraisal valuing the property at $755,000, though he testified that he knew it was not an accurate appraisal. Hale found a buyer, Dean Paul, to serve as straw man in the Etta’s Place transaction.
During the time that the Etta’s Place transaction was being worked out, Tucker told Hale that Madison owned the sewer and water system at Castle Grande, and that Madison needed to divest itself of this property before an upcoming federal regulatory examination, because Madison was not supposed to own a utility. Tucker was to set up a corporation to buy the sewer and water system. To finance the sale, the corporation would borrow the down payment from Capital Management and the rest of the purchase price from Madison.
Tucker incorporated Castle Sewer and Water Corp., naming two of his -employees, Dwight Harlan and Lorita King, as president and secretary. Tucker owned two-thirds of the stock and the other third was owned by R.D. Randolph, a MeDougal associate. *1021Tucker then submitted a loan application to Capital Management asking for a loan of $150,000, or $300,000 if possible; In the loan application, Tucker stated that the loan proceeds would be used “for initial operating capital and maintenance and painting of the [water] storage tank.” Hale stated that at the time he received the application, he knew that this statement in the application was false, because the real purpose of the loan would be to make the down payment on the water and sewer facilities. With the loan application, Tucker submitted a proposed, or pro forma, balance sheet showing what Castle Sewer and Water’s financial condition would be if it received the proposed $300,000 loan. The pro forma balance sheet showed as assets both the water and sewer facility, valued at $1.5 million, and the $300,000 in proceeds from the loan. In fact, in order to obtain the sewer and water facility, the corporation would have to use the $300,000 as a down payment, and so would never have both the facility and the $300,000 cash at the same time. Therefore, Tucker’s pro forma balance sheet overstated the corporation’s assets by $300,000 and hid the fact that the loan from Capital Management was to be used as a down payment on the facility.
Capital Management made the loan to Castle Sewer and Water in the amount of $150,000. The loan closed the same day as the straw man’s purchase of Etta’s Place. Tucker received the check, personally endorsed it and deposited it in a Castle Sewer and Water bank account.
Tucker did not undertake any personal obligation in connection with the purchase. The co-owner of Castle Sewer and Water Corp., R.D. Randolph, signed a personal guaranty of the corporate debt to Madison, although he testified at trial that he did not realize he had done so at the time. Tucker later gave his stock to Randolph, who actually ran the utility for some time. Randolph made some interest payments on the loan from Capital Management, but eventually the corporation defaulted on the debt. Randolph discharged the guaranty through personal bankruptcy.
After the Castle Sewer loan was made, Hale filled out and mailed to the Small Business Administration a Form 1031, which was required by the administration for every loan. The Form 1031 required a statement of the purpose of the loan. Hale filled in the purpose: “working capital.”
Hale testified that Tucker was angry when he discovered that Susan McDougal had drawn a real estate commission on Madison’s sale of the sewer and water facility to Castle Sewer and Water Corp. and that James McDougal had received a sizable bonus because of the sale. Hale testified that Tucker complained to him that the McDougals’ “commissions could get us all put in jail.” Later, Hale said Tucker called him from the governor’s mansion, upset by newspaper articles about the Castle Sewer and Water loan. Hale said that Tucker said the article had some facts that no member of the Arkansas press had the “IQ high enough to dig ... out.” Tucker told Hale not to talk to the press about the transaction, and he, Tucker, would “shut the locals down.”
Although there was a great quantity of evidence of other transactions, in light of the district court’s dismissal of Counts 8-11 and the jury’s acquittal of Tucker on Counts 2-4 and 20-21, it is unnecessary to recite it.
I.
Tucker’s most substantial argument is that the district court erred in denying Tucker’s motion for a new trial on the grounds of alleged misconduct of Juror Renee Johnson Hayes in failing to respond to questions on voir dire and in engaging in private communications about the case during trial.
A.
(1.)
Johnson’s juror questionnaire contained answers that she was single, that questions concerning a spouse were not applicable, and that she had one three-month-old child. In response to a question asking whether “any member of your family had ever been charged with a crime,” she stated that a member of her family had a drug conviction and was serving four years. She stated that *1022she had not formed an opinion regarding the guilt or innocence of any of the defendants.
During the district court’s comments to the jury following the reading of the indictment in the voir dire examination, the judge repeatedly emphasized the need for the venire members to reveal possible sources of bias during voir dire and gave them multiple opportunities to disclose anything that could have any bearing on their partiality.3
The judge assured the venire members that they could bring up matters privately:
But let me admonish you that in the event there is a question that you feel that you would like to respond in private, you make that request, I’ll consider , it, and we will retire to chambers.
The prosecutor then addressed a group of four jurors including Ms. Johnson, in a small group:
I want to cast this question in the broadest terms as possible, and I have touched on this specifically with regard to the areas we’ve covered before now, but is there anything that comes to mind of any of you, Mr. Swope, is there anything you can tell us that would affect your ability to serve fairly and impartially in this case? It may not be something I’ve asked you about directly but it may be something that is in the back of your mind, hasn’t come up before now, hasn’t occurred to you before now, before your opportunity to tell about it now, and maybe it’s something you don’t want to talk about publicly. If that’s the case, we can make arrangements to tell the Court outside the public forum. This is true for each of you. Is there anything that you can bring to our attention that would affect your ability to serve fairly and impartially in this ease. Mr. Swope?
A. No, sir.
Q. Ms. Johnson?
A. No.
Counsel for Tucker asked that same group of four jurors:
Q. As you sit here this afternoon is there anything at all, and I’m saying you are the only one that knows this, is there anything at all negative that you harbor about him?
Q. Ms. Johnson?
A. I have no opinion:
Q. As I asked the others, I will ask you, just examine yourself. What do you think? How do you feel? How do you feel about Governor Tucker?
A. I have no opinion. I don’t know.
Q. You have no feelings at all?
A. Yes, I have feelings.
Q. Tell me what those are.
A. About Governor Tucker? I guess he’s been a good governor.
No one asked Ms. Johnson any question particularly directed to the statement in her questionnaire that a member of her family *1023had previously been convicted of drug charges.
(2.)
After trial, Tucker filed a new trial motion alleging that he learned after trial that Juror Renee Johnson married Charles Marvin Hayes during the trial.4 Tucker’s motion alleged that he had reason to believe that Hayes was the father of Juror Johnson’s child.
Tucker’s motion contained detailed factual allegations. It stated that there was reason to believe that Hayes’s mother was Emma Ruth McIntosh Hayes,5 which would make Charles Hayes the nephew of Robert “Say” McIntosh. Hayes had been convicted of possession of two kilograms Of cocaine and received a forty year sentence. He was arrested and convicted together with Maurice Dan Crawford and Tommy McIntosh,6 the son of Say McIntosh, who would have been a first cousin of Charles M. Hayes. While Tucker was serving as Acting Governor of Arkansas, State Senator William L. Walker, Jr., asked Tucker to exercise executive clemency in favor of Hayes. Tucker sent Hayes a letter denying his application for executive clemency. Later, when Tucker was Governor, under the Arkansas Constitution State Senator Jerry Jewell became Acting Governor whenever Tucker left the state of Arkansas. When Tucker left the state to attend President Clinton’s inauguration, Jewell, as Acting Governor, granted executive clemency to Tommy McIntosh. As a result of instructions given by Tucker to his chief of -staff, Hayes did not receive clemency from Jewell.
Hayes thereafter received habeas relief and was released from imprisonment. See Hayes v. Lockhart, 989 F.2d 505 (8th Cir.1998) (unpublished).
Tucker’s motion alleged that when Juror Johnson was before the court on voir dire she must have known that Tucker had denied clemency to Hayes, but, when Johnson was asked about any prejudice against any party, she said nothing about Hayes or his history with Tucker.
Tucker’s motion alleged that Say McIntosh, Hayes’s uncle, had made frequent public demonstrations of hatred and contempt for Tucker, including demonstrations in front of the courthouse. Tucker submitted the affidavits of two Arkansas policemen reporting that Say McIntosh “frequently distributed leaflets attacking Governor Tucker” and “has appeared frequently at public events where Governor Tucker was present, criticizing the Governor, and on occasion been very loud and disruptive.” Appended to the affidavits were fliers, said to be representative of those Say McIntosh routinely distributed. The fliers accused Tucker of racism in failing to exercise clemency for a black prisoner sentenced to death and compared Tucker’s criminal activity to the prisoner’s, labeling Tucker “A Real Thief.” One flier stated: “Our governor who has 14 felony indictments will kill an innocent man just for racist reasons, and try to make some white jury sympathetic of his 14 indictments.” .The flier concluded:: “If the governor goes through with the lulling of Barry Lee Fairchild, every ounce of blood shed on the streets of Little Rock, the Governor, Jim Guy Tucker, will be sadly responsible for.”
Tucker alleged that he had information that Juror Johnson received communications during trial from Hayes and/or Tommy McIntosh regarding the matters on trial, and in support he filed the affidavit of State Senator William L. Walker, Jr., who had requested clemency for Hayes, Tommy McIntosh, and Maurice Crawford. Walker stated that he “personally vigorously advocated to Governor Tucker on behalf of all three men.” Walker recounted the story of *1024how Acting Governor Jewell commuted McIntosh’s sentence, but not Hayes’s. Walker stated, “I know that as a result of action taken by Governor Tucker, Hayes and Crawford remained in prison.” Walker said, “Hayes expressed anger over the denial of his applications.” Walker said he knew that during Tucker’s trial, Hayes told Tommy McIntosh that Hayes’s wife, Renee Hayes, was on the Tucker jury. Walker also said that during the course of the trial Tommy McIntosh called him and- said, “[W]e have someone on the jury.” Walker took McIntosh to mean that the McIntosh family had someone on the jury. Walker said he knew that Tommy McIntosh talked several times with Hayes, and that Hayes discussed the trial with his wife during the trial.
Tucker filed his own affidavit, recounting how he was able to prevent Jewell from commuting Hayes’s and Crawford’s sentences by instructing his chief of staff to tell Senator Jewell that no commutation could be granted if the prisoner’s files were not in his office.
Tucker alleged that if Juror Johnson had revealed her relationship to the Hayes case at voir dire, Tucker could have successfully challenged her for cause. He alleged that her presence on the jury denied him his right to a fair trial.
(3.)
On August 1, 1996, the district court conducted a hearing. Before taking evidence, the court stated that it was persuaded that Tucker had not submitted specific evidence demonstrating impropriety on the part of Juror Johnson or the entire panel and that Tucker had only submitted rank hearsay based on speculation and conjecture. “ Erring on the side of caution,” however, the court granted a hearing at which the jurors, including Juror Johnson, could be examined under oath to allow the United States to demonstrate that no extraneous evidence entered into the jury room during deliberations. The court stated that it would track the decision of the Eighth Circuit in United States v. Swinton, 75 F.3d 374 (8th Cir.1996). The court determined that Tucker’s counsel would be allowed to cross-examine, but limited such examination to the area developed by the government. Tucker’s counsel asked for clarification of the scope of the hearing, stating that Tucker’s motion had two thrusts—one that Juror Johnson was candid on voir dire, and the other that she was “in touch” with Charles Marvin Hayes, whom she married during the trial. The court responded that Tucker would be limited to the extraneous evidence issue, but that Tucker could proffer anything he liked for the Court of Appeals in the form of a summary, but not in the form of questions and answers.
At the hearing, Renee Johnson Hayes testified that at the time she served as juror she did not know that her husband had ever applied for executive clemency while he was in prison. She did not know her husband while he was in prison. She testified that at the time she served as a juror, she was not aware that Governor Tucker had denied her husband’s clemency petition and therefore never told any other juror that Tucker had denied her husband clemency.
On cross-examination, Johnson testified that she had become engaged to marry Hayes in 1994, but they had “never set a date.” Tucker’s counsel was permitted to establish that she had lived with Hayes, but counsel was not permitted to ask how long she had lived with him. Johnson said she knew when she began to live with Hayes that he had been in the Arkansas prison. She also knew Hayes had an uncle named Say McIntosh, but she did not know him.
Counsel began to inquire about her answer to the jury questionnaire item asking whether “any member of [her] family [had] ever been charged with a crime,” but the court prohibited the question on the ground that it was outside the scope of the hearing.
Counsel then asked Johnson whether she was aware that her husband’s uncle was picketing outside the courthouse during the trial, telling people that Tucker was a crook; the court again disallowed the question as beyond the scope of the hearing. Johnson said she knew of a mock cemetery Say McIntosh had set up on the south side of Little Rock, but she had not read any signs on it saying that Tucker was a crook, although she passed *1025the cemetery when she was going that direction.
Johnson said she had no contact with Tommy McIntosh. She said she knew that her husband was imprisoned as a result of an incident involving Tommy McIntosh, her husband’s cousin, and Maurice Crawford: She couldn’t say whether her husband is still in touch with Tommy McIntosh. Tucker’s counsel asked whether there had been any phone calls between Tommy McIntosh and her husband, and the court sustained an objection to the question.
Johnson testified that her husband never discussed Governor Tucker with her. Counsel asked whether she was aware of Say McIntosh’s animosity toward Tucker, but the court sustained the government’s objection to the question. She said she and her husband never discussed the trial in any manner, “not a word.” She said her husband never discussed with her the circumstances under which clemency was granted to Tommy McIntosh, but denied to Hayes himself, nor did he express bitterness about his unjust conviction on the drug charge. The 'court sustained an objection when counsel asked whether she and her husband had ever discussed his conviction on the drug charge. She answered that she did not tell about her husband’s conviction when she filled out her jury questionnaire. When counsel asked if she told about the brother-in-law’s conviction, the government objected, arguing that Tucker had waived the right to inquire about the jury questionnaire by not asking about it at voir dire. The court sustained the objection.
Tucker’s counsel asked Johnson if she got married over a noon hour during the trial, and Johnson said she really didn’t know the time. Counsel asked if it was one of the days when “we had an hour and a half’ for lunch, and she said, “I think so.” She did not mention to any of the other jurors that she got married over the lunch break. Tucker’s counsel asked whether she considered herself part of a family with Charles Hayes and her child before the trial; the court sustained the government’s objection to that question.
The government then called the other jurors and asked whether any of them knew before reaching a verdict that Tucker had denied a petition for executive clemency for Renee Johnson’s husband, or whether this was discussed in the jury room. All answered no.' One juror testified that after the trial was over she had talked with Ms.. Johnson about Tucker’s position on executive clemency for Hayes. The court sustained an objection to further inquiry about that conversation.
At the conclusion of the evidence, the government stated that the record established that no extraneous matters were injected before the jury.
Tucker’s counsel then asked to make his proffer. Counsel stated that Tucker was prepared to prove everything alleged in the motion papers.
Additionally, counsel offered to prove that when Governor Tucker was out of the state and Jerry Jewell became Acting Governor, Jewell asked for Charles Hayes’s clemency file, but that Tucker’s staff kept the file away from Jewell so that he did not succeed in granting Hayes clemency. Tucker’s counsel stated that there would be testimony that the Hayes-Mclntosh family was aware that Tucker’s staff prevented Jewell from granting Hayes clemency that day. Counsel additionally stated that he would prove by Juror Johnson that she formed a family with Hayes some time around the beginning of 1994, and that they were living together as man and wife at the time of the voir dire. Tucker’s counsel proffered the birth certificate showing the birth of Johnson’s child, Taylor, in November, 1995, with the father shown as Charles Hayes. The Hayes-Johnson marriage license and Hayes’s ' prison records were also proffered. Counsel stated that Johnson’s sister, Celina, is married to Charles Hayes’s brother, Brian Hayes. Counsel offered to prove that the family visits back and forth. Counsel stated that telephone records would show telephone calls between Charles Hayes, Say McIntosh, and Tommy. McIntosh from .time to time. Tucker’s counsel further offered to prove that Reiiee Johnson’s answer to the jury questionnaire about family members who had been charged with crime related to her *1026brother-in-law, who was in prison on a drug charge, and not to her husband.
The court denied the new trial motion, because the court was not persuaded that the jury had access to extraneous evidence in deliberating on the verdict.
(4.)
Tucker argues that his Sixth Amendment right to an impartial jury was violated because Juror Johnson concealed her relationship to Hayes and the McIntosh family and because she was subjected to outside influence. These are two discrete legal theories, calling for proof of different facts. The first theory is juror bias; in other words, when Johnson arrived at voir dire, she had an existing bias that should have disqualified her from serving as a juror in this case, but that she concealed the bias during voir dire. The second theory is private communication, contact, or tampering with a juror—the allegation that Johnson discussed the trial during its pendency with someone who tried to influence its outcome.
B.
(1.)
Tucker bases his claim of concealed juror bias on McDonough Power Equipment, Inc. v. Greenwood, 464 U.S. 548, 104 S.Ct. 845, 78 L.Ed.2d 663 (1984). In McDonough, after a products liability trial, the plaintiff discovered that one of the jurors had failed to respond to a question during voir dire about whether any one in his family had had any serious accident. Actually, the juror’s son had suffered a broken leg in an explosion. The Court of Appeals held that the juror’s failure to respond showed bias, because it showed the juror had a particularly narrow concept of what constitutes a serious injury. 464 U.S. at 552, 104 S.Ct. at 848. Writing for a plurality of the Supreme Court, Justice Rehnquist stated:
We hold that to obtain a new trial in such a situation, a party must first demonstrate that a juror failed to answer honestly a material question on voir dire, and then further show that a correct response would have provided a valid basis for challenge for cause. The motives for concealing information may vary, but only those reasons that affect a juror’s impartiality can truly be said to affect the fairness of a trial.
Id. at 556, 104 S.Ct. at 850. Thus, Tucker would have to prove three things about the voir dire: 1) that Juror Johnson answered dishonestly, not just inaccurately;7 2) that she was motivated by partiality; and 3) that the true facts, if known, would have supported striking her for cause.
The district court did not allow Tucker .to put on evidence on the McDonough claim, but instead limited the new trial hearing to the extraneous evidence theory. The district court has broad discretion in handling allegations that jurors have not answered voir dire questions honestly, and we defer to its discretion in deciding whether a post-trial hearing is necessary. See United States v. Williams, 77 F.3d 1098, 1100 (8th Cir.), cert. denied, — U.S. -, 117 S.Ct. 392, 136 L.Ed.2d 308 (1996). That discretion is not unlimited, however, and a movant who makes a sufficient showing of McDonough-type irregularities is entitled to the court’s help in getting to the bottom of the matter. In United States v. St. Clair, 855 F.2d 518 (8th Cir.1988), the defendant discovered after trial that a juror had not responded to a voir dire question about whether anyone had experience with explosives, although the juror had seven years’ such experience. The district court failed to permit the defendant to question the juror under oath “as to his *1027reasons for holding back this pertinent information, and his ability in having reached a guilty verdict without relying on his specialized knowledge.” Id. at 523. We reversed the district court and ordered a new trial. Id Accord United States v. Boney, 68 F.3d 497, 502-03 (D.C.Cir.1995) (party with Mc-Donough claim entitled to cross-examine juror; limited inquiry permitted by district court “virtually assured that the hearing would fail to discover any possible prejudice”) Therefore, taking into account the district court’s discretion in responding to the situation, we must nevertheless examine Tucker’s motion papers and proffer of evidence to determine if he made a sufficient showing to entitle him to a McDonough hearing.
In his new trial motion, Tucker contended that Juror Johnson deceived the court by not responding to the general questions about sources of bias and by giving an incomplete response to the question about whether “any member of your family” had ever been charged with a crime. Tucker contended that Johnson shared a familial relationship with Hayes in fact if not in law, and that this relationship was so important that Johnson deceived the court in not revealing Hayes’s conviction or her relationship to him.
Although Tucker asks us to order a new trial, the present state of the record is not complete enough to warrant such a drastic step. Any evidence that Johnson deceived the court is only circumstantial. As for her failure to respond to the numerous general questions about sources of bias, the only direct evidence is that Johnson herself was unaware of any grudge her husband and his family harbored against Tucker. She testified that she did not know Hayes until he got out of jail, and that at the time she served as a juror, she did not know Governor Tucker had denied her husband’s clemency petition. Even more categorically, she denied that she and her husband had ever discussed Governor Tucker. She testified they never discussed the trial in any manner, “not a word.” Significantly, one fellow juror testified that after the trial she and Johnson had discussed Tucker’s denial of clemency to Hayes, but the district court cut off questioning before counsel could find out what Johnson said. Tucker had subpoenaed Hayes, but the court did not permit Tucker to examine him as part of the proffer.
On this record, we cannot say that Tucker has established that Johnson deceived the court, but only that he made enough of a showing to entitle him to a hearing arid findings of fact on this issue. Johnson’s own testimony indicates that she was in a state of complete ignorance about events that nearly caused her husband to spend much of his life in prison. On the other hand, Tucker offered affidavits that indicated that Johnson’s husband and extended family were quite preoccupied with those very events. According to Tucker’s proffer, Hayes expressed anger to Walker over the denial of his applications for clemency. During the trial, Hayes’s uncle Say McIntosh was outside the courthouse decrying Tucker. Tucker’s affidavits contain fliers McIntosh distributed in Little Rock, characterizing Tucker’s denial of clemency to a black prisoner as racist and juxtaposing the innocence of the prisoner with Tucker’s guilt. One flier specifically derides Tucker’s expectation of a “sympathetic” white jury. According to Tucker’s proffer, Say McIntosh’s acrimony arose at least in part from Tucker’s role in denying Hayes and Crawford clemency and in stymieing their backup plan of receiving relief from Jewell when Tucker left the state. The information in Tucker’s proffer is very difficult to reconcile with Johnson’s testimony that she knew nothing about her family’s grudge against Tucker. Tucker has raised enough question about what Johnson knew at the time of voir dire to entitle him to a full hearing on this issue, including crucial credibility determinations.
Apart from her failure to respond to questions about whether she had any bias, Tucker also contends that Johnson intentionally failed to identify Hayes as a family member in order to conceal her relationship with him. Specifically, Tucker argues that she deceived the court in failing to report Hayes’s conviction in the questionnaire item about whether she had any family member who had been charged with a crime. Johnson testified at the hearing that her response on the questionnaire, “Drug conviction—guilty (serving *1028four years),” did not refer to Hayes, who originally had a forty-year sentence and who was not in jail at the time of voir dire. Counsel offered to prove that Johnson’s questionnaire answer referred to her brother-in-law, who was in prison on a drug charge. The court would not permit Tucker’s counsel to ask Johnson whether she considered herself to be part of a family with Hayes at the time of the voir dire.
The government argues that Johnson’s answer to the questionnaire was accurate because she was not married to Hayes at the time of the voir dire and therefore he was not her family. The government’s argument receives some support from United States v. Wright, 119 F.3d 630, 636 (8th Cir.1997), in which a juror faded to respond to a question asking whether he was related to any “law enforcement officer.” His uncle was a tribal children’s court judge. We said the juror “could have honestly believed” that a tribal court judge was not a law enforcement officer, so we rejected the defendant’s claim of bias without a hearing. Id. (citing Bolin v. Black, 875 F.2d 1343, 1350 (8th Cir.) ( no need for hearing to ascertain juror’s subjective honesty when juror’s answer was literally true), cert. denied, 493 U.S. 993, 110 S.Ct. 542, 107 L.Ed.2d 539 (1989)). We do not believe Wright represents a per se rule that if a question is ambiguous, an answer that is correct under any interpretation of the question cannot be a “false” answer under Mc-Donough. Rather, in Wright the court made an assessment that the answer was a reasonable one. Moreover, the alleged misrepresentation in Wright was not particularly material and probably would not have led to a successful challenge for cause. See United States v. Humphreys, 982 F.2d 254, 261 (8th Cir.1992) (to obtain new trial, must show misrepresentation showed actual bias or prejudice), cert. denied, 510 U.S. 814, 114 S.Ct. 61, 126 L.Ed.2d 31 (1993); Coughlin v. Tailhook Ass’n, 112 F.3d 1052, 1062 (9th Cir.1997) (dishonesty limited to collateral matters; no relief granted).
In contrast to the facts in Wright, Johnson was alleged to have concealed a relationship of great significance to her and one that would have been of great significance to Tucker if he had known of it. According to Tucker’s proffer, Johnson lived with Hayes, had a child with him, and was only a few days away from marrying him at the time of voir dire. Whether a juror in such, a position would either understand Hayes to be included in the term “family” or at least would understand that the questionnaire meant to ask about people with whom she shared such a close relationship, is, we believe, an issue that requires further detailed inquiry. Therefore, we hold that Tucker made a sufficient showing to entitle him to a McDonough hearing on whether Johnson meant to deceive the court in her questionnaire answer.
If Tucker can prove that Johnson deceived the court at voir dire, he will also have to prove that she did so because of partiality, rather than for some reason that is irrelevant to the fairness of the trial. “The motives for concealing information may vary, but only those reasons that affect a juror’s impartiality can truly be said to affect the fairness of a trial.” McDonough, 464 U.S. at 556, 104 S.Ct. at 850. In St. Clair, we emphasized that the court should have questioned the juror to find out “his reasons for holding back ... his pertinent information,” 855 F.2d at 523. If Tucker can prove the facts alleged in his proffer, there will be a sufficient showing to support a finding that the incomplete answer was motivated by partiality. However, it is also possible that the evidence at a hearing could support a finding of some other motivation for incomplete answers, such as embarrassment. See United States v. Boney, 68 F.3d at 502 (once dishonesty shown, need further inquiry to determine whether dishonesty motivated by bias); United States v. Boney, 977 F.2d 624, 634-35 (D.C.Cir.1992) (same).
Finally, under the McDonough test, Tucker must prove that if Johnson had given complete and honest answers at voir dire, she would have been subject to challenge for cause.8 There are various grounds *1029for such a challenge, see 28 U.S.C. § 1865 (listing conditions that would disqualify a person for jury service); Humphreys, 982 F.2d at 260-61 (claim of juror disqualification because of felon status). The ground Tucker alleges is partiality, known at common law as a challenge for favor (which coincides to a large extent with the second element of the McDonough test). “[T]o challenge for cause, a party must show actual partiality growing out of the nature and circumstances of [the] particular case.” United States v. Bascope-Zurita, 68 F.3d 1057, 1063 (8th Cir.1995) (citation and internal quotations omitted), cert. denied, 516 U.S. 1062, 116 S.Ct. 741, 133 L.Ed.2d 690 (1996). The decision of whether a particular juror should be excused for bias is entrusted to the sound discretion of the district court, see Bascope-Zurita, 68 F.3d at 1063, although of course that discretion has limits. See Kirk v. Raymark Industries, Inc., 61 F.3d 147, 152-56 (3d Cir.1995) (reversing district court for failure to strike jurors whose comments showed they were biased), cert. denied, 516 U.S. 1145, 116 S.Ct. 1015, 134 L.Ed.2d 95 (1996). The matters asserted in Tucker’s proffer would support a decision by the district court to strike Juror Johnson for cause. See Cox v. Norris, 133 F.3d 565, 572 (8th Cir.1997) (“ample reason” to excuse juror for cause where “she was acquainted with, and had reason to have animosity toward, the prosecution.”); United States v. Campbell, 845 F.2d 782, 786 (8th Cir.) (juror properly excused for cause where parents-in-law had worked for defendant’s political campaign), cert. denied, 488 U.S. 965, 109 S.Ct. 490, 102 L.Ed.2d 527 (1988); United States v. Perkins, 748 F.2d 1519, 1532 (11th Cir.1984) (challenge can be for “remote” relationship with party).
Tucker has therefore made a sufficient showing of a McDonough claim to entitle him to a hearing on his claim that he was denied his right to an impartial jury.
The government contends that Tucker waived Juror Johnson’s bias by failing to ask questions about it in voir dire. Failure, to ask the questions necessary to expose bias at. voir dire can result in waiver of objections to a juror. See United States v. Williams, 77 F.3d 1098, 1100-01 (8th Cir.), cert. denied, — U.S. -, 117 S.Ct. 392, 136 L.Ed.2d 308 (1996); Johnson v. Armontrout, 961 F.2d 748, 754 (8th Cir.1992) (if defendant fails to object to juror, has Sixth Amendment claim only if proves actual bias). Nevertheless, the government’s argument is beside the point, because in this case Tucker asked the questions and he contends that Johnson gave incorrect or incomplete responses.9
Tucker contends that he has made a showing sufficient to compel a finding of partiality and that we should reverse his convictions outright. To the contrary, we have a woefully incomplete record, with most of Tucker’s allegations' supported only by his counsel’s narrative offer of proof. We cannot anticipate what facts a full hearing may bring out and what credibility determinations the district court will make. We therefore reject Tucker’s suggestion that we reverse or grant a new trial, and instead remand to the district court for a hearing on the issues we have outlined.
*1030(2.)
Tucker also contends that the district court wrongly prevented him from proving that Juror Johnson was subjected to outside influence during the trial. Before the hearing, the district court stated that it was convinced that Tucker had “not submitted any specific evidence demonstrating any impropriety on the part of juror Johnson, or the entire panel, but has submitted rank hearsay.” However, out of abundance of caution, the district judge allowed Tucker to examine Johnson and the other jurors on the model of the hearing prescribed in United States v. Swinton, 75 F.3d 374, 381-82 (8th Cir.1996), another case in which he served as trial judge. Swinton involved the jury’s consideration of an extraneous fact not in evidence, rather than an allegation that a juror was subjected to outside influence, as in this case. Id. at 381. Following the Swinton model, the district court focussed on what was said in the jury room, but largely excluded evidence of what was said to Juror Johnson outside the jury room. Tucker offered the affidavit of Arkansas State Senator Walker stating: “I know that Tommy McIntosh talked several times with Hayes and that Hayes discussed the trial with his wife during the trial.” However, the court did not allow Tucker to call Walker, Tommy McIntosh, or Charles Hayes to substantiate these assertions.
To gain a new trial on the ground of juror misconduct, a movant must present evidence that is not barred by Federal Rule of Evidence 606(b) and that establishes grounds recognized as adequate to overturn a jury verdict. See United States v. Caldwell, 83 F.3d 954, 956 (8th Cir.1996).
Rule 606(b) specifically allows a juror to testify “on the question 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.”
When there has been an outside intrusion into the jury’s privacy and secrecy during trial, a party is entitled to a new trial if he has been prejudiced by the impropriety. Under Remmer v. United States, 347 U.S. 227, 74 S.Ct. 450, 98 L.Ed. 654 (1954) (Rem-mer I):
In a criminal case, any private communication, contact, or tampering, directly or indirectly, with a juror during a trial about the matter pending before the jury is, for obvious reasons, deemed presumptively prejudicial, if not made in pursuance of known rules of the court and the instructions and direction of the court 'made during the trial, with full knowledge of the parties.
Id. at 229, 74 S.Ct. at 451; accord Caldwell, 83 F.3d at 956; United States v. Melius, 123 F.3d 1134, 1139 (8th Cir.1997), cert. denied, — U.S. -, 118 S.Ct. 871, 139 L.Ed.2d 767 (1998). Our circuit does not apply the presumption shifting the burden of proof to the government if the contact pertained to outside legal advice, not extraneous facts. See United States v. Hall, 85 F.3d 367, 371 (8th Cir.1996). We do not have sufficient facts before us to ascertain whether the presumption of prejudice should apply, since Walker’s affidavit does not reiterate the substance of the alleged communications between Johnson and Hayes. However, the type of contact suggested by the record is neither outside legal advice nor exposure to extraneous facts, but private communication, contact, or tampering. Tampering was exactly the sort of contact involved in Remmer I, in which the Supreme Court stated the presumption rule. See 347 U.S. at 229, 74 S.Ct. at 451. But whether the presumption shifts the burden of proof to the government or not, the ultimate question is the same: “Did the intrusion affect the jury’s deliberations and thereby its verdict?”' United States v. Olano, 507 U.S. 725, 739, 113 S.Ct. 1770, 1780, 123 L.Ed.2d 508 (1993).
We defer to a district court’s discretion in deciding how to handle allegations of intrusions on the jury. See Caldwell, 83 F.3d at 957; United States v. Williams, 97 F.3d 240, 246 (8th Cir.1996). However, if a party shows that outside contact with the jury presents a reasonable possibility of prejudice to the verdict, he is entitled to a hearing on the matter. See Remmer, 347 U.S. at 230, 74 S.Ct. at 450-51; Rushen v. Spain, 464 U.S. 114, 119-20, 104 S.Ct. 453, 456, 78 *1031L.Ed.2d 267 (1983) (per curiam); Smith v. Phillips, 455 U.S. 209, 215, 102 S.Ct. 940, 945, 71 L.Ed.2d 78 (1982); see generally United States v. Madrid, 842 F.2d 1090, 1093-94 (9th Cir.), cert. denied, 488 U.S. 912, 109 S.Ct. 269, 102 L.Ed.2d 256, 257 (1988); 26 Moore’s Federal Practice ¶ 633.07[1] and n. 3 (Matthew Bender 3d ed.1997). The Supreme Court “has long held that the remedy for allegations of juror partiality is a hearing in which the defendant has the opportunity to prove actual bias.” Smith, 455 U.S. at 215, 102 S.Ct. at 945. The Eleventh Circuit has summarized its cases on the parameters of the district court’s discretion in investigating allegations of juror misconduct:
Examination of all of the cited authorities ... leads us to the conclusion that the cases fall along a continuum focusing on two factors. At one end of the spectrum the cases focus on the certainty that some impropriety has occurred. The more speculative or unsubstantiated the allegation of misconduct, the less the burden to investi-gate____ At the other end of the continuum lies the seriousness of the accusation. The more serious the potential jury contamination, especially where alleged extrinsic influence is involved, the heavier the burden to investigate.
United States v. Caldwell, 776 F.2d 989, 998 (11th Cir.1985). In sum, the depth of investigation required depends on both the gravity of the alleged misconduct and the substan-tiality of the movant’s showing of misconduct.
In this ease, Tucker presented the affidavit of Walker, that Walker had knowledge that Hayes and Johnson had talked about the case. Walker’s affidavit must be contrasted to the anonymous tips discounted by the Eleventh and Fifth Circuits. See Caldwell, 776 F.2d at 999; United States v. Sedigh, 658 F.2d 1010, 1013-14 (5th Cir.1981), cert. denied, 455 U.S. 921, 102 S.Ct. 1279, 71 L.Ed.2d 462 (1982). Significantly, Walker had championed Hayes’s cause in the effort to obtain clemency, and Tucker had denied his request. Walker’s earlier alliance with the Mclntosh-Hayes family gives added credence to his report that they have engaged in wrongdoing.
The background of Walker’s assertions makes the alleged misconduct far graver than an ordinary case of husband and wife communication during trial. Cf. Caldwell, 83 F.3d at 956 (allegation that a juror’s husband was present in the jury room was too vague to warrant further investigation); United States v. Williams-Davis, 90 F.3d 490, 495-99 (D.C.Cir.1996) (juror’s contact with husband harmless, since juror did not appear to be influenced by husband’s “two cents’ worth”), cert. denied, — U.S.-, 117 S.Ct. 986, 136 L.Ed.2d 867 (1997). The allegations of ex parte contact must be viewed in light of the extraordinary saga of Hayes’s attempts to gain clemency; Tucker’s frustration of those attempts directly and then by hiding Hayes’s file from Jewell; and the McIntosh family’s campaign against Tucker. With these facts in the background, the assertion that Johnson and Hayes had discussed the case during the trial must be taken as an allegation of serious misconduct, with a significant potential for prejudice to Tucker. See Swinton, 75 F.3d at 381 (juror’s statement that another juror said defendant had criminal record holds sufficient potential for prejudice to require full hearing).
The district court’s investigation of the misconduct focussed on whether the contamination was spread throughput the jury, but the court foreclosed a thorough inquiry into the existence and effect of the alleged communication to Johnson. The district court underlined its narrow view of the issues presented in its written order denying Tucker’s new trial motion: “Each juror, under oath, denied knowledge of Tucker’s action in denying clemency of Johnson’s husband, and stated that the matter was never discussed during deliberations. Hence, the Court finds that no extraneous prejudicial information was improperly brought to the jury’s attention and that no outside influence was improperly brought to bear upon any juror.” The question of prejudice depends on whether “there is any reasonable chance that the jury would have been deadlocked or would have reached a different verdict but for the •fact that even one reasonable juror was exposed to prejudicial extraneous matter.” United States v. Hall, 116 F.3d 1253, 1255 (8th Cir.1997) (emphasis added), cert. denied, *1032— U.S. -, 118 S.Ct. 1106, — L.Ed.2d -(1998). Therefore, prejudice is possible even if Johnson was the only juror to be contaminated.
In extraneous evidence cases, we have looked to see the extent and timing of jury exposure to the extraneous fact. See United States v. Blumeyer, 62 F.3d 1013, 1017 (8th Cir.1995), cert. denied, 516 U.S. 1172, 116 S.Ct. 1263, 134 L.Ed.2d 212 (1996); Hall, 85 F.3d at 371. This is simply part of the calculation in determining how much weight to accord one improperly received fact in the context of a trial’s worth of other facts. Contamination of a different kind occurs when, rather than being exposed to a fact not in evidence, a juror is subjected to psychological pressure by an outsider trying to coopt that juror’s vote. In such a case, the effect on the particular juror is intense and can be harmful to the litigants, even though the rest of the jury remains unaware of the impropriety and even though no extraneous evidence is admitted. For instance, in Remmer v. United States, 350 U.S. 377, 76 S.Ct. 425, 100 L.Ed. 435 (1956) (Remmer II), the Supreme Court vacated the conviction and ordered a new trial because an outsider had made an overture of a bribe to one juror. The district court had found that the incident was harmless because it did not affect the integrity of the jury’s deliberations. Id. at 379, 76 S.Ct. at 426. The Supreme Court reversed, holding that the bribery attempt did indeed affect the state of mind of the one juror involved, and that this deprived the defendant of a fair trial. “[The juror] had been subjected to extraneous influences to which no juror should be subjected, for it is the law’s objective to guard jealously the sanctity of the jury’s right to operate as freely as possible from outside unauthorized intrusions purposefully made.” Id. at 382, 76 S.Ct. at 428. More recently, in United States v. Cheek, 94 F.3d 136 (4th Cir.1996), the .Fourth Circuit held that a habeas petitioner was entitled to relief because of an implicit bribery attempt directed at one juror by a co-defendant. On habeas, the district court held the incident was innocuous because the juror was not exposed to extraneous facts, he did not tell the other jurors about the incident, and he testified that he listened to all the evidence and based his vote on the evidence. Id. at 141. The Fourth Circuit reversed, holding that the evidence showed the juror was “devastated and fearful” after the incident. Id. at 144. “Objectively, there is at least a reasonable possibility that the extraneous contact affected the verdict.” Id. Similarly, in United States v. Maree, 934 F.2d 196, 202 (9th Cir.1991), the Ninth Circuit held that there was actual prejudice where a juror was subjected only to “aggressive” comments on the case by her friends, without any additional extraneous facts or contamination of the rest of the jury. See also Church v. Sullivan, 942 F.2d 1501, 1508 (10th Cir.1991) (habeas petitioner entitled to hearing on whether jurors were exposed to jailer’s wife’s expressions of moral outrage); Stockton v. Virginia, 852 F.2d 740, 742, 746 (4th Cir.1988) (habeas granted where jurors exposed to opinion in diner that “they ought to fry” petitioner), cert. denied, 489 U.S. 1071, 109 S.Ct. 1354, 103 L.Ed.2d 822 (1989). Thus, a hearing limited to the issues of whether the other jurors were exposed to extraneous facts was not suited to the kind of impropriety alleged in this ease—intense emotional pressure brought to bear on one juror.
Johnson testified that she and her husband did not talk about the- case during the trial, and the other jurors testified that she had not mentioned anything about her husband. However, the court denied Tucker the opportunity to test that evidence by examining Walker, Tommy McIntosh, and Charles Hayes, whom Tucker has reason to believe could tell a different story from Juror Johnson’s. We conclude that a defendant who makes an allegation of serious misconduct by a juror, supported by evidentiary materials with significant indicia of reliability, is entitled to a more thorough investigation of his complaint than merely asking the juror whether he committed the misconduct. In United States v. Brantley, 733 F.2d 1429, 1439 (11th Cir.1984), cert. denied, 470 U.S. 1006, 105 S.Ct. 1362, 84 L.Ed.2d 383 (1985), after an allegation that one juror had informed the others of a fact not in evidence, the district court questioned the juror, who denied the misconduct. The court only permitted the parties to submit written ques*1033tions and refused to ask many of the questions submitted by counsel. The Eleventh Circuit held that a more searching inquiry was required, since the juror’s “natural inclination would be to deny making those remarks.” Id. at 1440-41. See also United States v. Boney, 68 F.3d at 502-03. We do not suggest that a juror’s testimony on the subject of his own conduct is “inherently suspect,” Smith, 455 U.S. at 217 n. 7, 102 S.Ct. at 946 n. 7, but only that, since other sources of evidence are available, Tucker should be allowed to use them.
We therefore remand with instructions that the district court permit Tucker a hearing on the private communication, contact, or tampering issue, with the opportunity to examine Walker, Tommy McIntosh, and Hayes on the subject of private communications to Juror Johnson during trial and the effect of any such communications on Johnson’s ability to serve impartially.
II.
Tucker contends that there was not sufficient evidence to convict him.
In reviewing a claim of insufficiency of the evidence, we view the evidence in the light most favorable to the government, with all reasonable inferences and credibility determinations made in support of the jury’s verdict. See Glasser v. United States, 315 U.S. 60, 80, 62 S.Ct. 457, 469, 86 L.Ed. 680 (1942); United States v. Liebo, 923 F.2d 1308, 1311 (8th Cir.1991). We must uphold the verdict if any reasonable jury could have found the elements of the crime beyond a reasonable doubt. Liebo, 923 F.2d at 1311. Conversely, we will reverse orily if the" jury must have had a reasonable doubt about an essential element of the crime. Id.
Additionally, once the existence of a conspiracy has been established, even slight evidence connecting a particular defendant to the conspiracy will suffice to prove involvement. See United States v. Maza,' 93 F.3d 1390, 1399 ( 8th Cir.1996), cert. denied, — U.S.-, 117 S.Ct. 1008, 136 L.Ed.2d 886 (1997).
Tucker attacks his conspiracy conviction,10 saying that there is no evidence that he . was anything but a bystander to a conspiracy between Hale and James McDougal. Tucker contends that the conspiracy was said to be for the benefit of “the political family,” and there was no reliable evidence that Tucker was related to that family. This argument ignores the whole context of the “political family” remark. At the same meeting, indeed in the same sentence in which Hale said McDougal referred to the “political family,” McDougal said specifically, “Jim Guy is going to need some funds ...” There is no ambiguity about whether the conspiracy, as reported by Hale, was meant to include and benefit Tucker.
Tucker also points out that on cross examination, Hale undermined his own testimony about the meeting around Tucker’s kitchen table. Tucker’s counsel asked Hale about a television interview he had given about when the “political family matter” first came up, in which he indicated that it may have been in a phone call or meeting after that evening meeting around the kitchen table.
Q: But you don’t know whether it came up with Jim Guy there or not, do you?
A: Not positive. You’re right.
This uncertainty is powerful ammunition that could have severely damaged Hale’s credibility in front of the jury. However, we believe it stops short of rendering Hale’s testimony insufficient to support the verdict. Hale’s credibility was for the jury to determine. Even without Tucker’s presence for the “political family” remark, Hale’s testimony still establishes that he, McDougal, and Tucker arranged the Castle Sewer and Water transaction so as to conceal the fact that Capital Management was providing the down payment for a business in which Tucker made no investment. According to Hale, the Castle *1034Sewer and Water plan was first revealed to him by Tucker himself, who said that he was undertaking the transaction because it was urgent for Madison to divest itself of the sewer and water system to avoid trouble with the regulators. Hale said he talked to Tucker about it more than once and that Tucker said: ‘We need to get this loan done for MeDougal. He’s really got problems and we need to at least show some type of due diligence.” Tucker described to Hale the transaction, including the hundred percent financing of the purchase, and Tucker “prepared most all of the [loan] documents.” Though the conversation around Tucker’s kitchen table may have summed up the government’s theory of the conspiracy in a nutshell, the case does not stand or fall on Tucker’s presence at one conversation. “The agreement which lies at the heart of any conspiracy case need not, of course, be expressly stated. Instead, the Government must only establish a tacit understanding between the parties, and this may be shown wholly through the circumstantial evidence of [the defendant’s] actions.” Bass, 121 F.3d at 1220 (internal quotation omitted). Hale’s testimony, together with the transactions that took place, provides abundant evidence of a conspiracy to extract money from Madison and Capital Management by fraud. Once the conspiracy is established, even slight evidence will suffice to connect the defendant with the conspiracy. Mazo, 93 F.3d at 1399. There is more than slight evidence that Tucker voluntarily linked himself with the scheme.
Tucker contends that he was not proved to be a member of the conspiracy because he had no “stake” in the cycle of benefits conferred by the interlocked transactions. Tucker contends he did not receive any benefit from the Etta’s Place transaction,11 because the Castle Sewer and Water loan closed on February 28, 1986, and the Etta’s Place proceeds were not deposited to Capital Management’s account until April 2, 1986. This argument ignores the role of James MeDougal as source of the Etta’s Place money and ultimate beneficiary of the Castle Sewer and Water loan. According to Hale, Tucker’s purchase of the sewer and water system was an accommodation of McDougal’s need to get ownership of the utility out of Madison Financial. Therefore, Hale’s fraudulent loan to Tucker to finance the purchase of the sewer and water system was a way of benefitting MeDougal indirectly. In turn, MeDougal was about to finance an extremely lucrative transaction for Hale’s benefit. Participation in the Castle Water and Sewer transaction may not have been to Tucker’s great advantage, but there is certainly evidence that he was a knowing participant in the scheme, rather than a bystander. It is not necessary to show that Tucker profited in order to prove he was part of the conspiracy.
Moreover, it is not true that Tucker had nothing to gain from the conspiracy, since there was evidence of a pattern of favors and reciprocal obligations running between James MeDougal and Tucker. For instance, Hale said that on the night of the first meeting out at Castle Grande, it was mentioned that MeDougal was going to let Tucker put his cable television company at Castle Grande. There was also evidence that MeDougal had Madison loan Tucker money when Tucker was liable on a note in default at another institution. However, the money did not come without strings. Tucker had to buy from MeDougal the 34 acres near Castle Grande that Hale described as a “turkey.” Hale described a symbiotic relationship in which benefitting one conspirator would eventually work to the good of all.
Tucker also argues that the mailing of the Form 1031 did not satisfy the mailing element of 18 U.S.C. § 1341,12 citing United *1035States v. Maze, 414 U.S. 395, 94 S.Ct. 645, 38 L.Ed.2d 603 (1974). We have dealt at length with the identical argument in our decision in the case of Tucker’s co-defendant, Susan McDougal, filed today, and have concluded that the mailing of the Form 1031’s did indeed perpetuate a fraud. See United States v. McDougal, 137 F.3d 547, 555 (8th Cir.1997). We will not repeat what we have written there. The evidence showed that Tucker himself prepared the loan application hiding the fact that the purpose of the Castle Sewer loan was to make the down payment on a facility for a corporation in which there was no investor money, only loans from Madison and Capital Management. In this context, a jury could certainly conclude that Hale’s incorporation of the “working capital” language from Tucker’s application into the Form 1031 perpetuated - a falsehood to avoid scrutiny, by the Small Business Administration.
Finally, Tucker contends that the loan application offered into evidence was superseded by a different application, which was lost between the date of the transaction and the trial. He points to records showing that an associate in his firm spent time preparing a loan application for Castle Sewer and Water Corp. after the date Tucker submitted the application that was in evidence at trial. The billing records are a very thin reed on which to hang a theory of multiple, superseding loan applications, especially since the associate in question does not remember any such superseding application and since the trial revealed other instances of backdating., At any rate, Tucker’s argument is that the billing records could support an alternative version of the facts in which the Castle Sewer and Water Corp. transaction would not be fraudulent. However, under our standard of review of a jury verdict, we must resolve disputed facts in favor of the verdict, not against it. “The evidence need not exclude every reasonable hypothesis except that of guilt.” United States v. Termini, 992 F.2d 879, 881 (8th Cir.1993). There is sufficient evidence to support the conviction.
III.
Tucker argues that several eviden-tiary rulings were abuses of discretion. First, he argues that the district court abused its discretion in letting the government impeach James McDougal with a prior statement to the FB.I that Tucker was a “thief who would steal anything that wasn’t nailed down.” Tucker did not testify, so his credibility was not in issue. McDougal had initially testified that he had known Tucker thirty-five years and knew of nothing Tucker had ever done that was illegal. During the course of his testimony, McDougal denied participating in the various crimes he was accused of, stating that he had not entered a conspiracy with Tucker or committed wire fraud, etc. In cross-examination, the government gave notice that it wanted to use the statement to. the FBI for impeachment. Tucker objected vehemently, but the court permitted the use of the statement. The court gave a cautionary instruction:
The government is about to elicit certain information from Mr. McDougal to develop from a document a statement previously made by Mr. McDougal [that] might be inconsistent with the testimony that he has given already. ' Now, you are admonished, and I want to make this crystal clear, it is being received for one purpose and one purpose only, impeachment.
The district court’s decision to admit evidence is reviewed only for abuse of discretion. See United States v. Fairchild, 122 F.3d 605, 610 (8th Cir.1997), cert. denied,U.S.-, 118 S.Ct.- 1086, — L.Ed.2d-(1998). In this case, the impeachment was not a perfect fit with the statements the government now points to as prior inconsistent statements. The statement in the FBI report was vague, amounting to little more than name-calling, and was not directly contrary to, for instance, McDougal’s statement that he and Tucker had not committed wire *1036fraud. Nevertheless, we cannot say that the decision to allow the impeachment was an abuse of discretion. Moreover, the limiting instruction channeled the jury’s use of this evidence. See United States v. Delpit, 94 F.3d 1134, 1144-45 (8th Cir.1996).
Tucker also contends the district court abused its discretion in allowing testimony by William Watt that he did not believe a statement Tucker made about one of the transactions on which Tucker was acquitted. The district court admitted this evidence as lay opinion under Fed.R.Evid. 701. Regardless of whether this was an appropriate use of Rule 701, we can say that in light of Tucker’s acquittal on the substantive count and in the context of the entire trial, admission of Watt’s statement was harmless beyond a reasonable doubt. See Fed.R.Crim.P. 52(a); United States v. Cortez, 935 F.2d 135, 140 (8th Cir.1991) (opinion as to veracity of witness was harmless error), cert. denied, 502 U.S. 1062, 112 S.Ct. 945, 117 L.Ed.2d 114 (1992).
IV.
Tucker contends that the district court erred in denying his request for jury instructions about various regulatory requirements. Tucker contends that these instructions were appropriate because there had been testimony that various transactions were structured to avoid violating regulations or to conceal such violations.
A defendant who requests a specific instruction is entitled to an instruction that conveys the substance of his request if his request is timely, it is supported by evidence in the case, and is a correct statement of the law. See United States v. Darden, 70 F.3d 1507, 1544 (8th Cir.1995), cert. denied, 517 U.S. 1149, 116 S.Ct. 1449, 134 L.Ed.2d 569 (1996). The defendant is not entitled to any particular formulation, as long as the instructions given adequately convey the law. Id. We review the district court’s decision to give or deny an instruction for abuse of discretion, considering the court’s ruling in the context of the entire charge. See United States v. Lynch, 58 F.3d 389, 391 (8th Cir.1995); United States v. Parker, 32 F.3d 395, 400 (8th Cir.1994).
The court denied Tucker’s requests for instructions about the substance of particular regulations, but gave an instruction that was actually more to the point. The court instructed the jury:
You have heard testimony during this trial concerning certain federal and state regulations of financial institutions, including regulations of the Small Business Administration, the Federal Home Loan Bank Board, and regulations of the State of Arkansas concerning savings and loan institutions. Such federal and state regulations are civil, not criminal laws. Therefore, violation of any such regulations should not be considered by you as a violation of the criminal law.
This instruction correctly told the jury that regulatory violations were not elements of the charged crimes. In contrast, Tucker’s proposed instructions would have required even further instructions to avoid misleading the jury and would have focussed the jury’s attention on collateral issues. Tucker introduced evidence about one of these regulations; this was the appropriate way to undermine what he considers to be misleading testimony by Hale about the effect of such regulations on Tucker’s actions. The district court did not abuse its discretion in denying the requested instructions.
Tucker contends the district court erred in denying his proposed instruction number 7, to wit: “An act is done ‘wilfully’ if done voluntarily and intentionally with the purpose of violating a known legal duty.”13 Thus, Tucker wanted the court to instruct the jury that Tucker had to intend to break the law. “The critical inquiry [in mail fraud] is not whether [the defendant] intended to break the law, but, rather, whether he intended to defraud____” United States v. Wicker, 80 F.3d 263, 267 (8th Cir.1996) (in*1037ternal quotations omitted). Tucker’s requested instruction would have misled the jury, and therefore, the court did not err in declining to give it.
* * * ' * * *
We conclude that the district court did not err with respect to the issues discussed in parts II, III and IV, but remand with instructions that the district court conduct a full hearing on the issues discussed in part I pertaining to Juror Johnson.