
500 F.3d 257 (2007)
UNITED STATES of America
v.
Corey KEMP, Appellant
United States of America
v.
Janice Renee Knight, Appellant
United States of America
v.
Lavan Hawkins, Appellant
United States of America
v.
Stephen M. Umbrell, Appellant
United States of America
v.
Glenn K. Holck, Appellant.
Nos. 05-3477, 05-3561, 05-4623, 05-4717, 05-4846.
United States Court of Appeals, Third Circuit.
Argued June 5, 2007.
Filed August 27, 2007.
*258 *259 *260 *261 *262 *263 Lloyd G. Parry, Esq., Davis, Parry & Tyler, William R. Spade, Jr., Esq., Philadelphia, PA, for Appellant Corey Kemp.
Nino V. Tinari, Esq., Philadelphia, PA, for Appellant Janice Renee Knight.
Timothy K. Lewis, Esq. (Argued), Schnader, Harrison, Segal & Lewis, Washington, DC, Elizabeth K. Ainslie, Esq., Nancy Winkelman, Esq., Bruce P. Merenstein, Esq., Schnader Harrison, Segal & Lewis, Philadelphia, PA, Nathaniel E. Jones, Esq., James H. Fields, Esq., Jones & Associates, Baltimore, MD, for Appellant Lavan Hawkins.
Lawrence S. Lustberg, Esq. (Argued), Kevin McNulty, Esq., Gibbons, P.C., Newark, NJ, for Appellant Stephen M. Umbrell.
Kevin H. Marino, Esq. (Argued), John D. Tortorella, Esq., Marino Tortorella, Chatham, NJ, for Appellant Glenn K. Holck.
Robert A. Zauzmer, Esq. (Argued), Office of the United States Attorney, Philadelphia, PA, for Appellee United States of America.
*264 BEFORE: SMITH and COWEN, and SILER[*], Circuit Judges.

OPINION
COWEN, Circuit Judge.
After a wide-ranging investigation into corruption in Philadelphia city government, the federal government obtained convictions against Corey Kemp, the former treasurer of Philadelphia; Glenn G. Holck and Stephen M. Umbrell, former executives of Commerce Bank; La-Van Hawkins, a businessman from Detroit; and Janice Renee Knight, the nominal owner of a printing company named RPC Unlimited. The appellants challenge their judgments of conviction on a variety of fronts. For the reasons discussed below, we will affirm.

I.
A. The Charges
On November 2, 2004,[1] a grand jury in the Eastern District of Pennsylvania returned a 63-count indictment against Kemp, Holck, Umbrell, Hawkins, Knight, Ronald White, a Philadelphia-based lawyer with close ties to city government,[2] and four others whose cases proceeded separately. The centerpiece of the indictment charged Kemp, White, Holck, Umbrell, Knight, and Hawkins with conspiracy to commit honest services fraud in violation of 18 U.S.C. § 371. According to the indictment, White acquired control over Kemp's decision-making by making corrupt payments and gifts to Kemp, and then used that control to direct city contracts to companies that he favored. The indictment alleged that Hawkins aided this arrangement by funneling bribe money from White to Kemp, and that Knight, White's girlfriend, took advantage of White's control over Kemp by accepting a steady stream of city business through RPC Unlimited. Moreover, the indictment charged Holck and Umbrell with participating in the conspiracy by extending, through Commerce Bank, otherwise-unavailable loans to Kemp in exchange for preferential treatment from Kemp on official matters.
In addition to the conspiracy charge, the indictment also charged the defendants with numerous counts of honest services mail fraud, honest services wire fraud, extortion, and perjury. Of these charges, four groups are relevant to this appeal. First, Kemp was charged with two counts of honest services mail fraud for his role in an asset-locator business that he created and operated with his friend, Rhonda Anderson. Second, Holck and Umbrell were charged with eight counts of honest services wire fraud concerning their role in corrupting Kemp. Third, Hawkins was charged with two counts of aiding and abetting wire fraud, concerning his transfer of money to Kemp. Fourth, Hawkins was charged with four counts of perjury stemming from false statements that Hawkins allegedly made while testifying before a grand jury investigating this case.[3]
*265 B. The Government's Evidence[4]
Kemp, Hawkins, Knight, Holck, and Umbrell proceeded together to trial. Opening statements began on February 22, 2005, and the government presented its case over the next six weeks. Central to the government's case were tape recordings of scores of conversations between the defendants.

1. Evidence Concerning Kemp
The government overwhelmingly proved that White showered Kemp with gifts[5] and that Kemp permitted White to wield an untoward influence in selecting which companies would be selected for[6] or excluded *266 from[7] bond teams.[8] Kemp and White's relationship was accurately encapsulated by Kemp's statement, after informing White that White would be paid $35,000 to $40,000 for a city contract, "[Y]ou got your boy sitting in the Treasurer's seat, man!" (App. at 12473.)
The government also presented evidence concerning the asset-locator business that Kemp operated with his friend Anderson. Anderson testified that in November 2002, Kemp told Anderson that the treasurer's office had received a request from a company for a list of bondholders whose bonds had matured but who had not collected their money. Kemp told Anderson that the two of them should create a business offering the same service. Kemp and Anderson hoped to get paid by the bondholders for facilitating their recovery; Kemp and Anderson agreed that Kemp would receive 40% of the proceeds. Kemp "said that he would have to be paid in cash and that no one could really know about his interest in it because he was treasurer." (App. at 9006.) According to Anderson, Kemp would receive his share for providing the list of bondholders and generating the forms that had to be filed to permit the banks to pay on the bonds. Anderson ultimately initiated this business, using a company that she co-owned with another friend. She collected fees of $3,700 and $1,000, and paid Kemp, in cash, a total of $1,300 for his services.

2. Evidence Concerning Holck and Umbrell
The government showed that Holck and Umbrell, as executives of Commerce Bank, worked mightily to earn contracts and increase cash deposits from Philadelphia.[9] At the same time that they were soliciting this business, Holck and Umbrell extended five different loans to Kemp. The government contrasted Commerce's amenability to Kemp once he became treasurer to the fact that just before Kemp took that position, in September 2001, Commerce rejected Kemp's application for a $2,000 line of credit with a form letter. It was the government's position that Holck and Umbrell extended these loans to Kemp for the purpose of influencing his decision-making, while Holck and Umbrell claimed that the loans were made in the ordinary course of business. The government's evidence concerning these loans may be summarized as follows:
First, the government presented testimony demonstrating that Kemp introduced Paul Schnapp, a member of his family, to Umbrell, and requested a $10,000 loan for Schnapp. Schnapp had filed for *267 bankruptcy two years earlier, and his application for a similar loan had recently been rejected by Wachovia. Commerce required Schnapp's wife, Teresita, a recent immigrant to the United States with almost no credit history, to co-sign the loan. Schnapp's loan application indicated that his income was $10,000 a month, but the only supporting documentation demonstrated income in the past month of $1,800. The branch manager wrote to a colleague that "this comes from the top" and was an "easy one," and Schnapp was approved for an unsecured $10,000 loan days after applying. (App. at 16548.)
Second, Commerce provided Kemp with mortgages that allowed him to purchase a $225,000 house with no money down. On November 4, 2002, Umbrell reported to the chairman of Commerce that Kemp had requested a mortgage and that Umbrell and a Commerce mortgage representative would meet with Kemp the following day. Umbrell did meet with Kemp; however, instead of a mortgage representative, the third member of the group was White. The next day, Umbrell approved Kemp's request to be pre-qualified for a $227,000 mortgage. However, Commerce Bank's policy was only to provide letters of pre-qualification to those individuals with credit scores of at least 680, and Kemp's scores ranged from 456 to 526. The government presented evidence that this was not an official Commerce pre-qualification form, but was a singular letter created by Umbrell to benefit Kemp.
The initial mortgage was formally approved on November 18, 2002  before Kemp had even completed an application. Commerce submitted Kemp's application to its underwriting process, and the application was rejected by the program that Commerce used to rate loans. The report indicated that Kemp's and his wife's credit scores ranged from 440 to 528, that Kemp had a past-due liability to Wachovia of over $13,000, and that Kemp owed other creditors an additional $20,000. Thomas Conte, who was the operations manager of Commerce's mortgage department at the time Kemp's loan was processed, reviewed the underwriting results and also rejected the application. However, on December 3, 2002, Holck and Umbrell reversed Conte's decision and approved the loan. While the loan was initially contingent upon Kemp's repaying the $33,000 that he owed to creditors, a week later, Holck and Umbrell waived that condition. Conte testified that this process deviated from Commerce Bank's standard underwriting procedures.
On December 18, 2002, Commerce's consumer loan department began processing Kemp's second mortgage loan, for the additional 20% of the purchase price. Commerce's usual policy was to advance 100% financing only to individuals with a credit score of at least 650 and no charge-offs in the past seven years. Kemp clearly did not meet those requirements  his credit score, as calculated by this underwriting program, was 433, and his charge-off with Wachovia originated within the previous year  and the underwriting program rejected the application. Nevertheless, Umbrell authorized the loan on the basis of Kemp's "strong bank relationship," his position as treasurer, and his income. (App. at 16347-48.) Contrary to Umbrell's claim that Kemp had a strong relationship with Commerce, the government presented evidence that Kemp's account with Commerce usually contained less that $1,000.
Third, in March 2003, Commerce made a $21,300 automobile loan to Kemp. The applicable credit report showed that Kemp's credit score was 520, which was still below Commerce's standard requirement of 650, and that Kemp had a prior bad debt to Wachovia (as described above) and an additional prior bad debt to Summit Bank for *268 a 1990 Pontiac Grand Am. Again, the underwriting program did not approve the loan, and again, Umbrell overrode the declination, based on Kemp's "strong bank relationship" and "positive previous experience." (App. at 16361.)
Fourth, in June 2003, Commerce approved Kemp's request for a $480,000 construction loan for his church, which had been damaged by lightning. On June 23, 2003, Miriam D'Elia, an attorney at White's law office, who was handling the closing for Commerce, informed Kemp that the church would not receive any money until it provided all of its specifications and plans. Kemp then called Umbrell, and Umbrell agreed to disburse money to the church for previous expenses as long as Kemp provided invoices  even without providing proof that the church had paid those invoices. Kemp and the church's pastor then created false invoices so that the church could procure money for invented expenses.
The day after Kemp spoke to Umbrell, D'Elia informed Kemp that Commerce's closing agent, Valerie Coates, was "very concerned" that the church understood it would not receive any money at the closing. (App. at 12449.) Kemp told D'Elia that Umbrell had approved the church's obtaining money for costs, and D'Elia responded that Coates was "real upset about that." (App. at 12450.) Coates then joined the conversation, and stated to Kemp, "[Y]ou're not expecting any funding [at closing], correct." (App. at 12452.) Kemp responded that Umbrell had approved the church's being reimbursed for previous expenses, and Coates said, "Okay, he's gonna be a bad boy then." (App. at 12453.) Coates testified that this statement did not mean that Umbrell had acted inappropriately, only that this decision would complicate her work.
Kemp and Umbrell spoke again later that day. Kemp asked Umbrell if he would waive any of the closing fees, and Umbrell agreed to waive the $3,500 appraisal fee. The two then discussed the renewal of some of Philadelphia's certificates of deposit with Commerce. Kemp told Umbrell that Umbrell did not have to work with any of Kemp's subordinates on the deal, but should talk to Kemp himself, because "I want them to know that you are my f___king guy. . . . So you get special treatment." (App. at 12459.)
Coates then sent an email to Holck, asking him to approve the advance of 80% of the church's as-is value of $150,000; immediately thereafter, Holck approved. In the file notes for the loan, Coates wrote, "I did what I was told to do." (App. at 16409.) She testified that this did not denote that she was unhappy with what had occurred, only that her actions had been authorized.
Fifth and finally, on July 1, 2003, Umbrell called Kemp, and the two briefly discussed Philadelphia's deposits with Commerce, and then Kemp stated, "[M]y brother-in-law's looking to do a small personal loan. . . . What's the maximum he can do unsecured?" (App. at 12549-50.) Umbrell responded, "[H]ow much does he need, tell me what he needs, `cause then I'll know what pocket to put it in." (App. at 12550.) Kemp informed Umbrell that his brother-in-law had "shaky credit," Umbrell asked if it was "bankruptcy bad," and Kemp responded in the negative. (App. at 12550.) Umbrell responded, "What do you want to go back and promise him? . . . Is [$6,000] enough for you to go back with? . . . I'm trying to make you look good . . . how much do you want to . . . if you want to tell him seventy five hundred, tell him seventy five hundred." (App. at 12551.) The two ultimately agreed on $7,500, which, as the telephone call made clear, *269 Umbrell approved without so much as seeing an application or speaking to the borrower. The government presented evidence demonstrating that Holck, Umbrell, and Kemp all understood that in return for these loans, Commerce Bank would receive preferential treatment. Most significant were the circumstances surrounding the city's selection of Commerce to offer a $30 million line of credit in support of the Neighborhood Transformation Initiative (NTI). In order to select the bank that would offer this line of credit, the city instituted a bidding process, in which interested banks would submit competing financial plans to the city. Soon after Commerce's submission, Kemp told White to tell Commerce, in the future, not to submit its bid first, because then Kemp could tell White about the other bids so that Commerce could then bid accordingly. Later that day, White called Umbrell, and said, "Listen, uh, somebody told me to tell you that when you guys do these things, don't ever send your stuff in first." (App. at 12192.) Umbrell responded, "[Y]ou know I love you, right? . . . I know who told you that, . . . and I understand why." (App. at 12192.) White then called Holck and gave him the same advice. Holck replied, "I know, I know. Corey said to him not to." (App. at 12198.)
Initially, the two best bids came from Commerce and KBC Bank. KBC offered the lowest interest rate, but Commerce offered to defer interest for an initial period. Kemp told White that he planned to call Commerce and convince them to lower their interest rate, which he did, in a subsequent conversation with Holck. Thus, Commerce was given the opportunity to submit a second bid. Around this time Kemp met with Donald DiLoreto, a representative of Wachovia Bank, and they discussed the bidding. After their conversation, DiLoreto emailed Kemp asking if he could submit an improved bid. Kemp never responded.
After Commerce submitted its improved offer, Kemp asked his boss, Janice Davis, if they could award the line of credit to Commerce. Davis told Kemp that if one bank was permitted to rebid, every bank must receive the same opportunity. Neither Davis nor the representatives of the five banks who submitted bids expected that any bank would have a chance to enter a second bid. Nevertheless, on Davis's orders, Kemp opened another round of bidding.
After the second round of bidding began, Holck and Umbrell discussed the situation in a telephone call with White. Holck appeared confused by the process, stating "you know we made . . . the revised proposal to Corey? . . . And something's not smelling right." (App. at 12256.) White assured Holck and Umbrell that they did not have to worry. This was good advice: Commerce's new bid, which conformed to Kemp's demand, was the best one and Commerce won the line of credit. The government presented evidence demonstrating that none of the other banks received any inside information about what to bid. The corruptness of the process was starkly described in a telephone call between Kemp and Reverend Frank McCracken, where Kemp stated:
Listen [Commerce Bank] better take care of me man, I'm hooking 'em up. Did my thing. `Cause, I got a conference call at four, three thirty and that's on ah a line of credit. I got a thirty million dollar line of credit from Commerce Bank for the city. . . . Ah, it was a bid though, it was a bid. And they, um, they bid, they were they were like in second place right, so I called Steve and I said Steve, look, this is what you all *270 got to beat. See, you didn't hear it from me, but then they came back.
(App. at 12557-58.)

3. Evidence Concerning Hawkins
The government's evidence against Hawkins primarily concerned three events: Hawkins's providing Kemp with a check for $5,000 dated March 10, 2002; Hawkins's providing Kemp with a check for $5,000 dated September 25, 2002; and a meeting that Hawkins attended with Kemp, White, and businessman Aslam Khan. The government focused on these events in an attempt to prove both that Hawkins had joined the conspiracy and that he had committed perjury when he subsequently testified about these events before a grand jury.
The first check was dated March 10, 2002, was written on the account of one of Hawkins's companies, was made out to Kemp, and was signed by Hawkins. The government presented evidence that White, but not Kemp, was present in Detroit on March 10, that Kemp had been married 20 months prior to that time, and that Kemp successfully cashed the check.
When Hawkins testified before a grand jury about circumstances surrounding this $5,000 check, however, he claimed that White and Kemp were in Detroit because White was throwing a bachelor party for Kemp. According to Hawkins, Kemp and White went to Hawkins's office, and White asked Hawkins to write a $5,000 check for Kemp as a wedding present. Hawkins stated that the check was never cashed.
The second check was dated September 25, 2002, and was written on Hawkins's personal account. Hawkins filled out the entire check except for the payee information. The government showed that on September 25, Kemp, but not White, was present in Detroit. This check bounced twice, and was ultimately replaced by a wire transfer sent from Hawkins's account to Kemp's account. The government showed that White had written a check to Hawkins for $5,000 dated September 23, 2002.
During his grand jury testimony, Hawkins testified that on September 25, 2002, he and White were together in Detroit. He explained that he gave the check to White to give to an association of African-American newspapers, who had been helping him in ongoing litigation against Burger King. Hawkins stated that the $5,000 was supposed to be part of a $15,000 donation that he had promised to the association. When asked why White had so recently written Hawkins a check for $5,000, Hawkins answered that the check could either have been to reimburse him for the first check he wrote to Kemp or to repay part of the $40,000 that Hawkins had loaned to White. Hawkins testified that the loan had been made from cash that he kept in his drawer.
The third salient event concerned a business meeting between Hawkins, Khan, Kemp, and White. As background, the government showed that in 2002, Hawkins joined a venture that was seeking to purchase AFCE, which owned and operated restaurants such as Popeye's, Church's, and Cinnabon. The cost of this venture was estimated to be between $600 million and $1 billion. To raise this capital, Hawkins sought investments from pension funds, including Philadelphia's fund. To that end, on January 22, 2003, Hawkins and other members of his group met in White's office with White, Kemp, and Tony Johnson, Philadelphia's chief investment officer, and attempted to convince Philadelphia officials to invest. Two days after that meeting, Hawkins rented a private jet to transport Kemp and White to the Super Bowl, at a cost of approximately $58,000.
*271 In the spring of 2003, the AFCE deal stalled, and Hawkins redirected his focus to acquiring almost 100 Church's Fried Chicken franchises from Aslam Khan. On April 21, 2003, Hawkins discussed this deal with White. Hawkins explained that he needed to raise some money, and hoped to acquire an investment from Philadelphia's pension fund, which was controlled by Anthony Johnson. In a May 2, 2003 phone call, Hawkins told White that he was going to "need you to have Tony [Johnson] to come to New York." (App. at 12011.) White responded that if he could not get Johnson, he would bring Kemp; Hawkins was amenable to that alternative arrangement.
On May 6, 2003, Hawkins called White and reminded him of the meeting "that I needed you to have Corey at." (App. at 12033.) Hawkins explained that he just needed Kemp "to keep this guy in the hole," so that he would think that Hawkins was "gettin' 20 million." (App. at 12034.)
On May 8, 2003, Hawkins, Khan, White, and Kemp met in New York. Kemp, who apparently believed that the purpose of the meeting was to discuss the possibility of Church's expanding into Philadelphia, said that he was "speaking on behalf of the administration," and that "we will do whatever we can that's in our power in the City's Administration to help this along." (App. at 12057-58.) Hawkins then prompted Kemp that first, Hawkins needed to raise $40 million to purchase the existing franchises. Kemp replied that he liked what he had heard and promised to take the proposal back to the administration. Kemp's boss, Davis, testified that Kemp did not have the authority to talk about the city's pension funds and that she would have fired him if she knew about this meeting.
Hawkins also testified before the grand jury about this meeting. He explained that the meeting was held because Khan was interested in bringing Church's Chicken into Philadelphia, and he believed that White would be useful in accomplishing that goal. He testified that he did not know why Kemp was present, did not know in advance that Kemp would be there, and had only asked White to bring someone to the meeting who was familiar with the lay of the city and could describe potential franchise locations to Khan. Hawkins explained that Kemp had been present at the previous meeting in Philadelphia concerning Hawkins's attempted purchase of AFCE, and had, after completing a market survey, reported on the opportunities that were available for fast-food restaurants in Philadelphia.

4. Evidence Concerning Knight
Janice Knight, White's girlfriend, was the nominal owner of RPC Enterprises, a printing company. The government presented evidence that White worked tirelessly to ensure that RPC was chosen as the printer for bond deals, and acted as the de facto president of the company. Moreover, the government adduced testimony that RPC lacked the equipment to perform printing jobs itself, and instead, farmed the jobs out to a separate company in New Jersey. Instead of negotiating fees with RPC, Kemp simply informed RPC what the city's budget was, and paid RPC the maximum allotted. Thus, during the time that Kemp was treasurer, RPC charged the city for $308,000 of work, despite the fact that the New Jersey company had charged RPC only $89,000.
C. Allegations of Juror Misconduct and the Discharge of Juror 11
On April 13, 2005, the case was presented to the jury. On April 27, 2005, the District Court discharged a juror, concluding *272 that she was biased against the government.
The District Court had received its first indication that something was amiss with the jury on April 18, 2005. That afternoon, the court received two notes from jurors. The first note stated:
Your honor, the following note was handed to me in confidence and asked that you see it. I have read it and can confirm the statements were made.
The person mentioned is making the rest of the group retry the case in the jury room. We are at a stalemate in the deliberation process. Evidence is being produced at the juror's request and when it is produced, it is being disregarded. I feel that several jurors are removing themselves from the deliberation process because they feel this effort is futile. We are slowly losing jurors as the days go by, not for lack of interest or commitment to their civic duty but for the fact that nothing they can do or say will matter.
(App. at 10680.) The note also requested simple definitions of the terms "intent," "reasonable doubt," and "conspiracy."
The second note stated:
Dear Foreperson: I have concerns regarding our deliberations. I feel I must keep an open mind, evaluate the evidence and make an effort to remain neutral. When the following comments are made by a fellow juror, I have concerns about that person's motivation and honesty.
1. "The government lies. They always lie."
2. "English is his second language  he didn't understand what he was saying."
3. "How would you be! She was having chemotherapy!"
4. "I've interviewed many people and I know when they are on drugs."
I have tried to pass RPC book from RW's office to the person, they refuse to look at what I was referring to, sat back in chair, closed eyes and folding their arms across their chest.
I also resent the statement you are all benefitting from Ron White  two months of my civic duty should be ended with conversations with fellow jurors that have open minds. Perhaps I am trying to be too open minded. Any suggestions?
(App. at 10691-92.)
In response to these notes, the judge called the jury into the courtroom. Then, before re-instructing the jurors on intent, reasonable doubt, and conspiracy, he stated:
You have been terrific citizens. You have given up your daily lives to come in here and perform your civic duty. That is very, very important. That is appreciated by everyone. When you became jurors, you took an oath and your oath was to follow the law and part of that oath is to deliberate, and you must, as part of that oath, deliberate with each other and discuss the evidence and discuss the law and try to reach a verdict.
Now, in trying to reach a verdict, you should not give up any beliefs which you have that you believe are true and sincere and that you hold to be warranted as a result of sitting as jurors and listening to this case for the last eight weeks.
At the same time though, it is your duty and obligation as jurors to listen to what the other jurors say and to consider their arguments, to consider what they recall about the evidence, to consider what they recall about the law, to consider their evaluation of the witnesses and you should listen to each other and they should listen to you. So it's important that, in the deliberative *273 process, that all of you engage in this process of deliberating but if you have a sincere belief that the others are wrong and you are right, you are entitled to hold on to that and maintain that but you still have the duty to deliberate and discuss with each other what you believe the evidence is and why you believe it. That is part of the duty of each juror to deliberate and if you still, after doing that, you still have your own sincere belief and you believe you are right, you are entitled to maintain it but please remember, the duty to deliberate is part of your oath as being jurors.
(App. at XXXXX-XXX.)
The following day, the judge received two more notes. The first note stated:
I am finding it very difficult to deliberate with a juror who will not acknowledge any of the evidence. The juror has made comments when presented with the evidence, "show it to someone who cares." The juror has continually referred to notes and used them as the evidence, also crosses arms over chest, leans back into chair and closes eyes and will not look over the evidence. Has made comments about "government lying." "FBI is biased." And "one defendant has been on chemotherapy" and 11 of us are benefitting from Ron White, (i.e. the payment we are receiving from jury duty), using analogies that does not pertain to anything.
(App. at 10739.)
The second note stated:
I'm concerned with one of my fellow jurors' comments during deliberations. I know every juror has their right to state feelings and opinions. Some of the remarks that I've hear from one individual makes me feel as though there is more bias than normal deliberations, comments such as,
1. Prosecutors and FBI agents are liars.
2. Using sympathy and feelings as factors in deliberations.
3. Saying all the jurors are receiving benefits, courtesy of Ron White.
I don't know if I should be doing this but if I didn't, I don't think justice was served.
(App. at 10739-40.)
After receiving this note, the court heard argument from all counsel, and resolved to question each juror individually. The court asked three questions of each juror, in camera: (1) "Are you personally experiencing any problems with how the deliberations are proceeding without telling us anything about the votes as to guilt or innocence? If yes, describe the problem." (2) "Are all the jurors discussing the evidence or lack of evidence?" (3) "Are all the jurors following the court's instructions on the law?" (App. at 10758.) The jurors' responses may be summarized as follows:
Juror 1: There was a problem at one point, but at the moment all jurors were acting appropriately.
Juror 2: Juror 11 was very prejudiced against individuals based on their occupation.
Juror 3: While deliberations were stressful, all jurors were acting appropriately.
Juror 4: All jurors were properly discussing the evidence or lack of evidence, but sometimes certain jurors refused to look at evidence that other jurors found pertinent.
Juror 5: All jurors were acting appropriately.
Juror 6: All jurors were acting appropriately.
Juror 7: All jurors were acting appropriately.

*274 Juror 8: Juror 11 was refusing to consider evidence.
Juror 9: Juror 11 sometimes refused to look at evidence presented by other jurors, and was reasoning illogically. However, the jurors had made a break that day and it seemed that the deliberations were progressing.
Juror 10: All jurors were acting appropriately.
Juror 11: The jurors were making progress.
Juror 12: All jurors were considering the evidence, but one juror said that the prosecutors were lying and that all jurors were receiving benefits from Ron White.
The District Court decided, on the basis of these responses, that no further instructions were necessary. The next day the judge received a note stating "the hearing in your chambers has helped facilitate the deliberations." (App. at 10791.)
Despite these glad tidings, on April 25, the jurors passed a note to the judge stating:
Your Honor, deliberations have stopped! One of the jurors has changed their mind over the weekend on several counts that were decided last Thursday. The reasons stated by the juror are illogical. The following jurors do not believe further deliberations will be at all beneficial. It is unfair to the defendants, the lawyers, and the people of Philadelphia to continue deliberations in this manner.
(App. at 10862.7.) The note was signed by nine jurors.
Based on this note, the court decided to question the jurors individually a second time. The judge asked each juror: (1) "Is there any juror or jurors who are refusing to deliberate?" (2) "Is there any juror who is refusing to discuss the evidence or lack of evidence?" (3) "Is there any juror who is refusing to follow the Court's instructions?"
(App. at 10862.20.)
The jurors' responses are as follows:
Juror 1: Juror 11 did not seem to be deliberating, but was discussing the evidence and following the instructions.
Juror 2: Juror 11 was not cooperating and was refusing to discuss the evidence.
Juror 3: Three jurors were refusing to listen to the others, with Juror 11 particularly culpable.
Juror 4: Juror 11 was refusing to deliberate and discuss the evidence.
Juror 5: One juror was refusing to deliberate.
Juror 6: All jurors were acting appropriately.
Juror 7: Juror 11 was refusing to follow the court's instructions.
Juror 8: Juror 11 was refusing to deliberate and discuss the evidence.
Juror 9: Juror 11 was refusing to discuss the evidence.
Juror 10: All jurors were acting appropriately.
Juror 11: One or two jurors seemed to feel that they were done talking about certain topics.
Juror 12: Juror 11 was refusing to deliberate and discuss the evidence.
Immediately after completing this voir dire, the judge received a note stating that "the jury did not feel the right questions were asked." (App. at 10862.43.) The jurors suggested the following questions:
1. Why have the jurors stopped deliberating?
2. Are jurors looking at the evidence logically and forming a reasonable opinion about each individual count?

*275 3. Have jurors entered into deliberations with preconceived notions or prejudices?
4. Can you summarize the deliberations and how you feel they are progressing?
5. Are jurors using emotions rather than evidence to rule on certain counts? Most counts?
6. Your Honor, is it possible to allow the jurors to expand on their answers?
(App. 10862.43-44.) Upon receiving this note, the judge dismissed the jury for the day to allow himself time to consider how to proceed.
The next day, the judge provided additional instructions to the jurors. The judge first told the jurors that the questions he had asked the day before were "the only questions which [he felt he was] entitled to ask at that time," so as to avoid intruding into the jury deliberations. (App. at 10874.) He stated, however, that he could "ask questions to [ensure] that all of you are following your oaths as jurors, that you are reviewing the evidence, that you are deliberating with each other and that you are following my instructions." (App. at 10876.) The judge then reminded the jurors that they were under oath, and that they had promised to decide the case fairly and impartially without being swayed by either the race or the occupation of the defendants and witnesses. The judge reiterated that the jurors were prohibited from using prejudice or bias in making decisions, and explained that if any juror did so, that juror was not following his instructions. The court also re-instructed the jurors about their duty to deliberate, but emphasized that "if you come to different views of the facts, you are entitled to maintain those views as long as you consider the views of others." (App. at 10882.)
The next day (April 27), the judge received three notes. The first asked legal questions. The second was from Juror 11, and stated:
Is it permissible to discuss the fact that we have heard only selected portions of selected phone calls and to try to evaluate what this might mean in determining what was going on and what people intended to do?
Can you consider omitted evidence  for example, the prosecution only showed us what they wanted to show?
Is it permissible to try to illustrate how two people might understand a conversation differently?
(App. at 10896.)
The third note asked two preliminary questions, and then stated, "How do we inform the court a juror has violated his or her oath (i.e., biased against the government. States prosecution makes up stories)." (App. at 10896.) The court then instructed the jury about the legal questions contained in the notes, and concluded: "Ladies and gentlemen, as I said yesterday, bias is a violation of a juror's oath. If one of you or more of you believe that a juror is biased against the government, I instruct you to send me another note, saying that you believe that, and then the remedy is that I will have the jury come into the conference room again, one by one." (App. 10922.) After hearing argument from counsel, the court clarified a few points with the jurors, including the bias instruction. The court stated:
I want to make it clear that when we talk about bias . . . we are talking about bias against a specific type of person or against a specific occupation or bias against the prosecution and that the juror is unwilling to put aside that bias. If the juror or jurors say, they don't believe someone or a particular piece of evidence, that is not bias. That is just a *276 discussion on the evidence presented in the case. But as I said before, if there are jurors who believe that a juror is unwilling to put aside bias, is using bias, that is something you should send me a note about. . . .
(App. at 10935-36.)
Soon afterward, the court received two more notes. The first stated:
I believe the following statements reflect bias by a juror: The government lies. The prosecution made it up. They couldn't get Ron White so they made this up about Corey Kemp. They didn't play all of the calls. They omitted evidence. You didn't hear what they didn't want you to hear. The FBI lies. The government didn't present the evidence to prove anything.
(App. at 10949.) The second note, signed by the foreman, stated simply, "[A]sk the three questions again in your chambers." (App. at 10949.) Based on these notes, the court conducted another individual voir dire, which yielded the following information:
Juror 1: Juror 11 refused to deliberate and discuss the evidence, and would not put aside her bias.
Juror 2: Juror 11 refused to deliberate and discuss the evidence, and was very prejudiced against the government. Juror 2 also stated: "You just can't talk to [Juror No. 11]. She goes nuts. She starts banging on the table. She won't listen to us. Won't let anybody get a word in edge-wise. . . . If we present her with evidence, she flips through her notes and does not want to hear any evidence." Juror 2 went on to emphasize that "[Juror No. 11] is totally against the government. We have heard her say, the FBI are nothing but a bunch of liars."
Juror 3: Three jurors had a difficult time listening to each other, but Juror 11 just shut down and refused to look at evidence that was shown to her. Juror 11 was also off task and biased against the FBI and the government. Juror 3 also stated: "People disagree on a lot of things. But when the arguments are with 11, it's just like slamming your head into a wall."
Juror 4: Juror 11 refused to deliberate or discuss the evidence, and was biased.
Juror 5: All jurors were deliberating and discussing evidence, but Juror 11 was "a bit biased, not tending enough to the evidence and instructions."
Juror 6: All jurors were deliberating, and Juror 11 was not biased, but did refuse to look at the evidence.
Juror 7: All jurors were deliberating, but Juror 11 was refusing to discuss the evidence. Further, Juror 11 was biased to a point concerning witnesses's occupations and was allowing that to cloud her judgment. However, she was not letting it affect her "that much."
Juror 8: Juror 11 was refusing to deliberate and would not look at any evidence. She also was biased and unable to put that bias aside.
Juror 9: Juror 11 was refusing to deliberate and would not look at evidence that was presented to her. Juror 11 also held prejudices against the government or the FBI, and was unwilling to put those prejudices aside.
Juror 10: Juror 11 refused to deliberate, ignored evidence, carried a personal agenda, and was biased.
Juror 11: No jurors were refusing to deliberate or discuss the evidence. However, some people had difficulty focusing on the specific elements of a crime instead of just concluding that a defendant was guilty because the juror disapproved of the defendant's behavior. The jurors had been attempting to rule on guilt or innocence count by count, *277 which was difficult for her, because so many of the issues were interrelated. Once the jury began to evaluate evidence on a different issue, Juror 11 said, "[W]ait a minute here, this contradicts what we agreed to back here. . . . I agreed with you about here now I'm looking at this evidence and I don't think that is there anymore." All the jurors were working to put aside their biases. When asked whether she was biased against the FBI, Juror 11 responded that she didn't think so, and that her comments concerning the FBI were made only to refute another juror's statement that they only had to consider the FBI's evidence. She had not claimed that FBI agents always lie; instead, she had said that they are "probably accomplished liars" from doing undercover work, and that they are therefore probably skilled at detecting when someone is lying to them.
Juror 12: Juror 11 was refusing to deliberate or discuss evidence, and was biased against law enforcement. Speaking of Juror 11's bias, Juror 12 stated that "it's not the witnesses in the trial. It's the preconceived notion that law enforcement lies, they are telling lies."
Juror 11 then asked to return to clarify her previous statements. She stated that she had actually said that she "thought FBI agents were among the most credible witnesses because they were careful to say what they believed to be the truth and to distinguish fact from opinion." (App. at 11062.) She also claimed to have said that one agent may have been biased going into his interview with Janice Knight because he had previously heard so much incriminatory information about her.
To recap, eight jurors (1-4, 8-10, 12) stated in clear terms that Juror No. 11 violated her duty to deliberate in good faith and to be free of preconceived biases that informed her decision-making. Juror No. 11 denied any allegations of bias or a refusal to deliberate. Juror No. 5 stated that no juror was refusing to deliberate or discuss the evidence/lack of evidence, and that all the jurors were following the District Court's instructions. This juror also stated that Juror No. 11 was "a bit biased, not tending enough to the evidence and instructions, but we are working on that." Juror No. 6 stated that Juror No. 11 was not refusing to follow the instructions, and that she was not biased either. However, Juror No. 6 did note that Juror No. 11's answers were "pretty much set in stone," making it "hard to show her the evidence." Juror No. 7 stated that no juror was refusing to deliberate, although he believed that Juror No. 11 refused to consider the evidence or lack of evidence. Juror No. 7 also noted that Juror No. 11 expressed bias against certain occupations.
Based on these responses, the court granted the government's motion to discharge Juror 11. The court stated:
We have 11 out of the 12 jurors have made affirmative responses to at least one of the questions that I posited to them concerning juror number 11. . . . I find that the other 11 jurors are more credible than juror number 11. And to put it bluntly, I find that juror number 11 is in denial. She is articulate but she is not credible. You cannot balance her testimony that she made here against 11 of her fellow jurors. I find that they are more credible than she is, and I find that she is biased against the government. . . . I find that she has come in here and tried to articulate using an educated background. She is articulate but she is in total denial of what I find to be the facts as expressed by the other 11 jurors. . . .
(App. at 11079-80.)
The District Court then seated an alternate juror who had been sequestered during the first round of deliberations.
*278 D. The Verdict
On May 10, 2005, the reconstituted jury returned its verdict. Kemp was convicted of conspiracy, seven counts of wire fraud, 11 counts of mail fraud, one count of attempted extortion, one count of extortion, two counts of making false statements to a bank, and four counts of filing a false income tax return; Hawkins was convicted of one count of wire fraud and three counts of perjury; Holck and Umbrell were convicted of conspiracy and two counts of wire fraud; and Knight was convicted of two counts of making false statements to the FBI. The jury also acquitted the defendants or was unable to reach a verdict on a number of charges.[10]
Ultimately, the District Court sentenced Kemp to 120 months' imprisonment, Holck to 28 months' imprisonment, Umbrell to 27 months' imprisonment, Hawkins to 33 months' imprisonment, and Knight to 5.5 months' imprisonment. All five defendants then filed timely appeals.

II.
We have jurisdiction of an appeal from a judgment of conviction pursuant to 28 U.S.C. § 1291.

III.
The appellants challenge their convictions on many grounds. Kemp argues that the government failed to present sufficient evidence to support his convictions for mail fraud relating to his asset-locator business. Holck and Umbrell challenge their wire fraud convictions by arguing that the indictment failed to state an offense, the District Court erroneously instructed the jury, and the government presented insufficient evidence to sustain the convictions. Holck and Umbrell also argue that their conspiracy convictions must be vacated because there was a prejudicial variance between the crime charged in the indictment and the evidence adduced at trial. Hawkins claims that the government presented insufficient evidence to support his convictions for wire fraud and perjury, that the District Court's jury instructions on wire fraud omitted an essential element, and that the Court wrongly admitted several forms of unfairly prejudicial evidence. Finally, all appellants contend that the District Court erred by individually questioning the jurors upon receiving complaints of juror misconduct and then discharging Juror 11. We consider each of these sundry claims in turn.
A. Kemp's Mail Fraud Convictions
Kemp claims that the government presented insufficient evidence to support his convictions for honest services mail fraud concerning his role in the asset-locator business for which he received $1,300. We review sufficiency-of-the-evidence challenges with particular deference to the jury's verdict. United States v. Dent, 149 F.3d 180, 187 (3d Cir.1998). Because Kemp did not raise this argument to the District Court in his motion for acquittal, we review for plain error. United *279 States v. Vampire Nation, 451 F.3d 189, 203 (3d Cir.2006). Plain error requires: "(1) an error; (2) that is plain; and (3) that affected substantial rights." Id. As we will explain, the jury's conclusion on this count was supported by the evidence and not plain error.
To prove mail fraud, the government must establish "(1) the defendant's knowing and willful participation in a scheme or artifice to defraud, (2) with the specific intent to defraud, and (3) the use of the mails . . . in furtherance of the scheme." United States v. Antico, 275 F.3d 245, 261 (3d Cir.2001). Congress has clarified that "the term `scheme or artifice to defraud' includes a scheme or artifice to deprive another of the intangible right of honest services." 18 U.S.C. § 1346. Honest services fraud, in turn, typically occurs in either of two situations: "(1) bribery, where a [public official] was paid for a particular decision or action; or (2) failure to disclose a conflict of interest resulting in personal gain." Antico, 275 F.3d at 262-63. The government pursued both of these discrete theories in prosecuting the mail fraud counts at issue.
Kemp maintains that his convictions must be vacated because the government presented insufficient evidence to prove honest services fraud under either the bribery theory or the failure-to-disclose theory.[11] Because Kemp challenges the sufficiency of the evidence of these two theories, and has not argued that either was legally invalid or unconstitutional, we will affirm if the evidence is sufficient to support a judgment on either theory. See United States v. Syme, 276 F.3d 131, 144 (3d Cir.2002) (explaining that "if the evidence is insufficient to support a conviction on one alternative theory in a count but sufficient to convict on another alternative theory that was charged to the jury in the same count, then a reviewing court should assume that the jury convicted on the factually sufficient theory and should let the jury verdict stand").
Here, a reasonable jury could conclude beyond a reasonable doubt that Kemp "was paid for a particular decision or action," Antico, 275 F.3d at 263, and thus convict him of honest services fraud under a bribery theory. The government presented evidence that Kemp and Anderson had an arrangement where Anderson would locate owners of unredeemed city bonds and attempt to help them cash their bonds. This project required Kemp to exercise his authority as treasurer: he provided Anderson with a list of holders of outstanding bonds and a form letter for her to use; also, the treasurer's office was responsible for contacting the banks to facilitate the ultimate repayment. When Anderson was asked at trial what Kemp would contribute to the business to earn his share of its proceeds, she identified only these first two official actions. A reasonable jury certainly could have concluded that Kemp was paid for the reasons that Anderson pinpointed  taking official action that aided the business.
Kemp argues that he was paid not for taking particular actions but because he held a stake in the business. However, Anderson testified that the company was formally owned by her and a friend, and not Kemp. While Kemp did suggest the idea of the asset-locator business to Anderson, a reasonable jury could have found it more likely that Kemp was paid $1,300 for taking actions in favor of the *280 business than for providing an inchoate idea.
We have repeatedly recognized that accepting money in exchange for an official action is a form of honest services fraud.[12]See United States v. Panarella, 277 F.3d 678, 690 (3d Cir.2002); Antico, 275 F.3d at 262-63. As Pennsylvania law provides, "public office is a public trust and . . . any effort to realize personal financial gain through public office other than compensation provided by law is a violation of that trust." 65 Pa. Cons.Stat. § 1101.1. Here, the government presented sufficient evidence for a reasonable jury to find beyond a reasonable doubt that Kemp violated that trust by soliciting and accepting payment in exchange for taking official action. Accordingly, we find no plain error and reject Kemp's challenge to his mail fraud convictions.
B. Holck's and Umbrell's Wire Fraud Convictions

1. Challenge to the Indictment
Holck and Umbrell lead off their attack on their wire fraud convictions by arguing that their convictions under the bribery theory of honest services fraud must be vacated because that theory was not charged in the indictment. We deem an indictment sufficient so long as it "(1) contains the elements of the offense intended to be charged, (2) sufficiently apprises the defendant of what he must be prepared to meet, and (3) allows the defendant to show with accuracy to what extent he may plead a former acquittal or conviction in the event of a subsequent prosecution." United States v. Vitillo, 490 F.3d 314 (3d Cir.2007) (internal quotation marks omitted). Moreover, "no greater specificity than the statutory language is required so long as there is sufficient factual orientation to permit the defendant to prepare his defense and to invoke double jeopardy in the event of a subsequent prosecution." United States v. Rankin, 870 F.2d 109, 112 (3d Cir.1989). We exercise plenary review over this challenge. United States v. Hedaithy, 392 F.3d 580, 590 n. 10 (3d Cir. 2004).
We conclude that the indictment here adequately charged Holck and Umbrell with the bribery theory of honest services wire fraud. The wire fraud counts of the indictment (counts 15-22) plainly alleged honest services fraud, charging Holck and Umbrell with engaging in "a scheme to defraud the City of Philadelphia and its citizens of the right to defendant COREY KEMP'S honest services in the affairs of the City of Philadelphia." (App. at 587.) Then, the specific factual allegations  some of which were incorporated by reference to the allegations of the conspiracy charge, see Fed. R.Crim.P. 7(c)(1) ("A count may incorporate by reference an allegation made in another count."); see also United States v. Markus, 721 F.2d 442, 444 (3d Cir.1983)  were sufficient to alert Holck and Umbrell that the government planned to pursue both theories. The indictment refers to "the benefits that HOLCK and UMBRELL extended to Kemp with the intent to influence KEMP's official actions" (App. at 491), and charges that "defendants GLENN K. HOLCK and STEPHEN M. *281 UMBRELL, on behalf of their employer, Commerce Bank, provided benefits to Kemp in the form of otherwise unavailable loans in exchange for favorable decisions by KEMP as Treasurer of Philadelphia" (App. at 554). These allegations were sufficient to charge Holck and Umbrell with honest services fraud under a bribery theory, and accordingly, we reject Holck and Umbrell's argument that the indictment should have been dismissed.

2. The "Stream of Benefits" Instruction
Holck and Umbrell next claim that the District Court misstated the law when instructing the jury on the bribery theory of honest services fraud, such that the jury was invited to convict if it concluded that Holck and Umbrell had provided benefits to Kemp in a "general attempt to curry favor." We exercise plenary review over whether the District Court correctly stated the law, and consider "whether the charge, taken as a whole, properly apprise[d] the jury of the issues and the applicable law." Armstrong v. Burdette Tomlin Mem'l Hosp., 438 F.3d 240, 245 (3d Cir.2006) (alteration in original) (internal quotation marks omitted).
While we agree with Holck and Umbrell that bribery may not be founded on a mere intent to curry favor, we nevertheless reject their challenge to the District Court's instructions. As Holck and Umbrell recognize, there is a critical difference between bribery and generalized gifts provided in an attempt to build goodwill. The Supreme Court has explained, in interpreting the federal bribery and gratuity statute, 18 U.S.C. § 201, that bribery requires a quid pro quo, which includes an "intent `to influence' an official act or `to be influenced' in an official act." United States v. Sun-Diamond Growers of Cal., 526 U.S. 398, 404, 119 S.Ct. 1402, 143 L.Ed.2d 576 (1999) (quoting 18 U.S.C. § 201(b)). This may be contrasted to both a gratuity, which "may constitute merely a reward for some future act that the public official will take (and may already have determined to take), or for a past act that he has already taken," and to a noncriminal gift extended to a public official merely "to build a reservoir of goodwill that might ultimately affect one or more of a multitude of unspecified acts, now and in the future." Id. at 405, 119 S.Ct. 1402. This discussion is equally applicable to bribery in the honest services fraud context, and we thus conclude that bribery requires "a specific intent to give or receive something of value in exchange for an official act." Id. at 404-05, 119 S.Ct. 1402.
Holck and Umbrell arrive at their conclusion that this requirement was elided by the instructions only by reading certain sections of the jury charge out of context, which "is not the way we review jury instructions, because a single instruction to a jury may not be judged in artificial isolation, but must be viewed in the context of the overall charge." United States v. Park, 421 U.S. 658, 674, 95 S.Ct. 1903, 44 L.Ed.2d 489 (1975). Read fairly, the instructions proffered by the District Court repeatedly emphasized the critical quid pro quo, explaining that "[t]o establish such bribery the government must prove beyond a reasonable doubt that there was a quid pro quo, . . . that the benefit was offered in exchange for the official act." (App. at 9642.) The Court continued, "where there is a stream of benefits given by a person to favor a public official, . . . it need not be shown that any specific benefit was given in exchange for a specific official act. If you find beyond a reasonable doubt that a person gave an official a stream of benefits in implicit exchange for one or more official acts, you may conclude that a bribery has occurred." (App. at 9643.) Finally, the Court explained, *282 "[t]o find the giver of a benefit guilty, you must find that the giver had a specific intent to give . . . something of value in exchange for an official act, that is, that the accused had the specific intent to engage in such a quid pro quo exchange." (App. at 9643-44.) This instruction correctly described the law of bribery, and left no danger that the jury would convict upon merely finding that Holck and Umbrell provided benefits to Kemp in a general attempt to curry favor or build goodwill.
Moreover, we agree with the government that the District Court's instruction to the jury that it could convict upon finding a "stream of benefits" was legally correct. The key to whether a gift constitutes a bribe is whether the parties intended for the benefit to be made in exchange for some official action; the government need not prove that each gift was provided with the intent to prompt a specific official act. See United States v. Jennings, 160 F.3d 1006, 1014 (4th Cir.1998). Rather, "[t]he quid pro quo requirement is satisfied so long as the evidence shows a `course of conduct of favors and gifts flowing to a public official in exchange for a pattern of official actions favorable to the donor.'" Id. Thus, "payments may be made with the intent to retain the official's services on an `as needed' basis, so that whenever the opportunity presents itself the official will take specific action on the payor's behalf." Id.; see also United States v. Sawyer, 85 F.3d 713, 730 (1st Cir.1996) (stating that "a person with continuing and long-term interests before an official might engage in a pattern of repeated, intentional gratuity offenses in order to coax ongoing favorable official action in derogation of the public's right to impartial official services"). While the form and number of gifts may vary, the gifts still constitute a bribe as long as the essential intent  a specific intent to give or receive something of value in exchange for an official act  exists. This theory was accurately and entirely presented to the jury in the jury instructions, and accordingly, we reject Holck and Umbrell's argument that the instructions as proffered were inadequate.

3. Legal Validity of Failure to Disclose Theory
Holck and Umbrell next present three arguments that the District Court's jury instructions concerning the failure-to-disclose theory of honest services fraud were legally erroneous. If, as Holck and Umbrell argue, the alternative theory is legally invalid, we must vacate their convictions. See Syme, 276 F.3d at 144. Our review over whether the District Court correctly stated the law is plenary. Armstrong, 438 F.3d at 245. For the reasons discussed below, we conclude that the District Court correctly charged the jury.
Holck and Umbrell first argue that the jury instructions were inconsistent with our decision in Panarella. According to Holck and Umbrell, when we held in Panarella that a "public official who conceals a financial interest in violation of state criminal law while taking discretionary action that the official knows will directly benefit that interest commits honest services fraud," 277 F.3d at 694, we ruled that the discretionary action must benefit the public official himself, and not the person or organization that provided the benefit. They thus argue that the District Court's instructions, which permitted the jury to convict upon finding that Kemp took "a discretionary official action benefitting the giver of the benefit" (App. at 9644), wrongly stated the law.
A complete analysis of Panarella plainly demonstrates the defectiveness of Holck and Umbrell's position. In Panarella, *283 Loeper, while Majority Leader of the Pennsylvania Senate, worked as a business consultant for a tax collection business. Id. at 681. Loeper failed to disclose his income from the business as required by state law, and spoke and voted against bills that would have harmed that business. Id. We held that this conduct constituted honest services fraud, and emphasized the importance of disclosing conflicts of interest. Id. at 696-97. We explained:
Were it easy to detect and prosecute public officials for bribery, the need for public officials to disclose conflicts of interest would be greatly reduced. . . . One reason why federal and state law mandates disclosure of conflicts of interest, however, is that it is often difficult or impossible to know for sure whether a public official has acted on a conflict of interest. The only difference between a public official who accepts a bribe and a public official who receives payments while taking discretionary action that benefits that payor, as Loeper did in this case, is the existence of a quid pro quo whereby the public official and the payor agree that the discretionary action taken by the public official is in exchange for payment. Recognizing the practical difficulties in proving the existence of such a quid pro quo, disclosure laws permit the public to judge for itself whether an official has acted on a conflict of interest.
Id. at 697 (emphasis added) (citation omitted). This explanation is consistent with our opinion in Antico, where we emphasized, broadly, the duty of a public official "to disclose material information affecting an official's impartial decision-making." 275 F.3d at 264. Accordingly, we reject Holck and Umbrell's argument that the discretionary action must directly benefit the public official, and hold that honest services fraud encompasses a situation where a public official conceals a financial interest in violation of state criminal law while taking discretionary action that the official knows will directly benefit the individual or organization behind that financial interest. We thus reject Holck and Umbrell's challenge on this front.
Holck and Umbrell next argue that the jury instructions misstated the law because they did not require the jury to find that Holck and Umbrell failed to disclose a financial interest in violation of a state criminal law. However, this argument misapprehends Pennsylvania's statutory structure. The District Court read to the jury the provisions of 65 Pa. Cons.Stat. § 1103(a)-(c), all of which are felonies. See 65 Pa. Cons.Stat. § 1109(a). Thus, we also reject this claim.
Finally, Holck and Umbrell contend that the District Court's instructions about the species of loans that public officials are required to report were incomplete. They argue that in addition to the proffered instructions, which stated that "a commercially reasonable loan made in the ordinary course of business" is exempt from the reporting requirement,[13] the District Court should have informed the jury that "the financial terms of the loan must be below-market or that the loan must be outside the ordinary course of business."
To the extent that the language proposed by Holck and Umbrell adds anything to the District Court's instruction, we conclude that the District Court was not obligated to include it. Holck and *284 Umbrell's authority for their position  4 Pa.Code § 7.153(b)(3) and Executive Order No. 16-92  concerns gifts that public officials are prohibited from accepting, and are thus inapposite here. The crucial issue is whether Kemp was required to report the loans; whether he was entitled to accept the loans is a different matter altogether. Accordingly, we conclude that the District Court correctly and fully[14] instructed the jury about the governing law concerning loans.

4. Sufficiency of the Evidence for Bribery Theory
Holck and Umbrell's final challenge to their honest services wire fraud convictions is that the government presented insufficient evidence to sustain those convictions under a bribery theory. According to Holck and Umbrell, the government failed to prove: (1) that they made a payment to Kemp; (2) that they received a benefit from Kemp; and (3) that the two were directly connected. As noted above, we will "view the evidence in the light most favorable to the Government and sustain the verdict if any rational juror could have found the elements of the crime beyond a reasonable doubt." United States v. Cartwright, 359 F.3d 281, 286 (3d Cir.2004) (internal quotation marks omitted).
As we held above, bribery requires a specific intent to give or receive something of value in exchange for an official act. We note that evidence of a "quid pro quo can be implicit, that is, a conviction can occur if the Government shows that [the defendant] accepted payments or other consideration with the implied understanding that he would perform or not perform an act in his official capacity." Antico, 275 F.3d at 257. As we have recognized, "`the official and the payor need not state the quid pro quo in express terms, for otherwise the law's effect could be frustrated by knowing winks and nods.'"[15]Id. at 258 (quoting United States v. Bradley, 173 F.3d 225, 231 (3d Cir.1999)).
We first reject Holck and Umbrell's argument that the benefits that they were accused of bestowing on Kemp  a variety of loans  cannot constitute bribes (or the quid of a quid pro quo) because they were made at the prevailing interest rates in the regular course of business. As a factual matter, a reasonable jury certainly could have found that these loans were not advanced in the usual course of business and were instead extended to Kemp and his friends solely because of Kemp's position. For instance, Umbrell agreed to loan $7,500 unsecured to a person Kemp described as having "shaky credit" without even seeing an application or speaking to the borrower. Umbrell's stated purpose for approving this loan was to make Kemp "look good." Moreover, Kemp's mortgage loans were approved by Holck and Umbrell before Kemp filed an application, and *285 despite the fact that Commerce's computer program and underwriter rejected the mortgages. Indeed, an underwriter from Commerce testified that the procedures used to approve this loan failed to comply with standard practice. This evidence is sufficient to support a jury's conclusion that these loans were made available to Kemp only because he was the treasurer.
Moreover, as a legal matter, we conclude that providing a loan to a public official (or his friends or family) that would have otherwise been unavailable to that official or available at a higher interest rate may constitute a bribe. This is consistent with our discussion in Antico where, concerning quid pro quo under the Hobbs Act, we broadly described a bribe as involving "payments or other consideration." Id. at 257 (emphasis added). Further, the conclusion comports with the federal bribery statute, which refers to "anything of value," and other general definitions of bribery. See, e.g., Black's Law Dictionary 186 (7th ed.1999) (defining "bribery" as "[t]he corrupt payment, receipt, or solicitation of a private favor for official action"). It also takes account of the commonsense notion that a loan may be of immense value to the recipient: for instance, here, Kemp's mortgage loan allowed him to purchase a house.
Our conclusion that a loan may constitute the quid in a bribery prosecution is also supported by the relevant caselaw. Most notably, in United States v. Gorman, 807 F.2d 1299 (6th Cir.1986), the defendant argued that a loan was not a "thing of value" under § 201 because he fully repaid the loan with interest. Id. at 1304. The Sixth Circuit rejected that argument, because at the time that the defendant received the loan he was having "severe financial difficulties" and it was unclear whether such a loan would have been available to him in the ordinary course of business. Id. at 1305. The court focused on the value that the recipient "subjectively attache[d] to the items received." Id. A loan was also recognized as a potential quid in United States v. Williams, 705 F.2d 603 (2d Cir.1983). There, a United States Senator was convicted under the federal bribery statute for "seeking funds for the financing and purchase of a mining venture in which he had an interest in exchange for his assistance in obtaining government contracts for the venture." Id. at 612. One of the two sorts of funds that the senator sought was a $100 million loan that was to be repaid with interest. Id. at 620. The court never questioned that the loan could serve as a bribe, and termed the evidence against the senator "overwhelming." Id. at 612; see also United States v. Crozier, 987 F.2d 893, 901 (2d Cir.1993) ("[A]s we have held in connection with § 201, any payment that the defendant subjectively believes has value, including a loan, constitutes a thing `of value' within the meaning of § 666(c)"). Thus, we conclude that loans, so long as they are granted in exchange for an official act, may drive a bribery prosecution.[16]
We also conclude that Holck and Umbrell's assertion that they did not receive any benefit from Kemp is contradicted by the record evidence. Despite Holck and Umbrell's protestations, a reasonable jury could undoubtably have concluded that Kemp provided a benefit to them when he rigged the bidding for the NTI line of credit in Commerce's favor. The government showed that after Commerce submitted its bid, Kemp told White to tell Holck and Umbrell not to submit their bids first, because then Kemp could tell *286 White about the other bids. This alone permitted a reasonable jury to conclude that Kemp intended to benefit Commerce to the detriment of other banks. Then Kemp called Holck and gave him specific instructions about how Commerce could tweak its initial bid to guarantee that its bid would win  a courtesy that he did not extend to any other bank. Indeed, when Wachovia attempted to rebid, Kemp ignored its request. While a second round of bidding was instituted  on the orders of Kemp's boss and against Kemp's wishes  only Commerce was told exactly what to bid to ensure success. This evidence was plainly sufficient for the jury to conclude that Holck and Umbrell received a benefit from Kemp.
Finally, we reject Holck and Umbrell's contention that the government failed to present evidence of a pro demonstrating that Holck and Umbrell extended loans to Kemp in exchange for favorable treatment. Especially damaging to Holck and Umbrell's position is the June 24, 2003 phone call between Umbrell and Kemp. There, Umbrell agreed to waive the $3,500 appraisal fee for the church loan, and then, while the two discussed the renewal of some of Philadelphia's certificates of deposit with Commerce, Kemp told Umbrell that Umbrell could always speak to Kemp directly because "you are my f___king guy. . . . So you get special treatment." While Kemp did not elaborate about why Umbrell was his "guy," the jury certainly could have inferred that it was because of the consistent flow of loans and perks  including the waiver of the appraisal fee discussed moments before  that Holck and Umbrell extended. The evidence also showed that not only did Kemp say that Holck and Umbrell would get special treatment  they did. The NTI bidding process is a particularly egregious example. Further, the government showed that Holck and Umbrell believed that they would receive this special treatment, as illustrated by the phone call between White, Holck, and Umbrell, where Holck appeared surprised that any bank besides Commerce would get a second opportunity to bid, stating that "you know we made . . . the revised proposal to Corey? . . . And something's not smelling right." Similarly, Kemp's explanation of the NTI transaction to his friend, in which Kemp stated that Commerce Bank had better take care of him because he hooked them up with the NTI deal, evinced his understanding that he was giving Holck and Umbrell special treatment in exchange for loans. This course of conduct permitted the jury to infer that Kemp had agreed with Holck and Umbrell that he would take official action in their favor in exchange for their providing him loans and benefits.
Accordingly, we conclude that the government presented sufficient evidence to support the jury's verdict against Holck and Umbrell on the honest services wire fraud charge.[17]
C. Holck's and Umbrell's Conspiracy Convictions
Holck and Umbrell argue that their convictions for conspiracy to commit honest services fraud must be vacated because *287 there was a prejudicial variance between the charge in the indictment and the proof presented at trial.[18] They claim that while the indictment alleged a single conspiracy involving Holck, Umbrell, White, Kemp, Hawkins, and Knight, the evidence adduced at trial proved, if anything, that Holck and Umbrell, Knight, and Hawkins each joined a separate conspiracy with White and Kemp. "A conviction must be vacated when (1) there is a variance between the indictment and the proof presented at trial and (2) the variance prejudices a substantial right of the defendant." United States v. Kelly, 892 F.2d 255, 258 (3d Cir.1989). As we discuss below, we agree with Holck and Umbrell that there was a variance; however, we will nevertheless affirm their convictions because they have failed to demonstrate prejudice.

1. Variance
There is a variance if the indictment charges a single conspiracy while the evidence presented at trial proves only the existence of multiple conspiracies. Id. We must determine "whether there was sufficient evidence from which the jury could have concluded that the government proved the single conspiracy alleged in the indictment." Id. Thus, we evaluate whether the record, when viewed in the light most favorable to the government, contains substantial evidence that Holck and Umbrell were part of a single conspiracy that also included Kemp, White, Hawkins, and Knight.
In order to determine whether a group of individuals engaged in a single conspiracy or multiple conspiracies, we evaluate three factors. We consider: (1) "whether there was a common goal among the conspirators"; (2) "whether the agreement contemplated bringing to pass a continuous result that will not continue without the continuous cooperation of the conspirators"; and (3) "the extent to which the participants overlap in the various dealings." Id. at 259 (internal quotation marks omitted). Here, the government has failed to satisfy the first Kelly factor.
The crux of Holck and Umbrell's argument is that the government charged a *288 hub-and-spokes conspiracy but failed to prove the existence of a rim connecting the spokes. That is, they claim that Kemp and White were the hub, and entered into separate agreements with three unconnected spokes  Holck and Umbrell, Knight, and Hawkins. This argument is predicated on the seminal case Kotteakos v. United States, 328 U.S. 750, 66 S.Ct. 1239, 90 L.Ed. 1557 (1946). Kotteakos involved an indictment that charged 32 individuals with conspiracy to obtain loans under a Fair Housing Act program by making false applications; Simon Brown was at the center of the alleged conspiracy, helping a disparate group of individuals obtain these loans. Id. at 752-53, 66 S.Ct. 1239. The Supreme Court held that the facts presented failed to prove a single conspiracy:
Except for Brown, the common figure, no conspirator was interested in whether any loan except his own went through. And none aided in any way, by agreement or otherwise, in procuring another's loan. The conspiracies therefore were distinct and disconnected, not parts of a larger general scheme, both in the phase of agreement with Brown and also in the absence of any aid given to others as well as in specific object and result. There was no drawing of all together in a single, over-all, comprehensive plan.
Blumenthal v. United States, 332 U.S. 539, 558, 68 S.Ct. 248, 92 L.Ed. 154 (1947) (discussing Kotteakos).
In Blumenthal, the Court found a single conspiracy where the defendants were all involved in a scheme to acquire whiskey and resell it above authorized prices. Distinguishing these facts from Kotteakos, the Court noted that all the conspirators "knew of and joined in the overriding scheme" and "sought a common end" to sell the whiskey, so that "the several agreements were essential and integral steps." Id. at 559, 68 S.Ct. 248. The contrast between Kotteakos and Blumenthal helps us to determine whether an impermissible variance has occurred. As this Court has noted, the Government may not charge "multiple unrelated conspiracies," but it can charge a "master conspiracy [with] more than one subsidiary scheme." United States v. Kenny, 462 F.2d 1205, 1216 (3d Cir.1972); see also United States v. Chandler, 388 F.3d 796, 811 (11th Cir.2004) (stating that "although each of these alleged spoke conspiracies had the same goal, there was no evidence that this was a common goal").
Here, Holck and Umbrell argue that they could not have joined the same conspiracy as Knight and Hawkins, because they neither knew about Knight's and Hawkins's activities nor were dependent on those activities. The government, on the other hand, argues that it proved both knowledge and interdependence.
First, we agree with Holck and Umbrell that the government failed to present evidence that they either knew or should have known about Knight's and Hawkins's activities. While the government claims that Holck and Umbrell acted "with knowledge that White was serving interests in addition to theirs," it presents no factual support for this assertion. Nor is this the type of conspiracy that must have had other members; it would have been perfectly reasonable for Holck and Umbrell to have believed that they were doing business with only Kemp and White. Cf. Chandler, 388 F.3d at 811 n. 21 ("In a drug conspiracy, in which the object of the conspiracy is clearly illegal and there are various clandestine functions to perform, the conspirators can be charged with knowledge that others are performing these different functions. In this case, however, such knowledge may not be imputed *289 to defendants since each of their redemptions was complete unto itself." (citation omitted)). This may be contrasted with Blumenthal, where three salesmen were convicted of conspiring to sell whiskey at above-ceiling prices in violation of the Emergency Price Control Act. 332 U.S. at 541, 68 S.Ct. 248. The Court held that while "each salesman aided in selling only his part," id. at 559, 68 S.Ct. 248, they could nevertheless form part of a single conspiracy, because they "knew or must have known that others unknown to them were sharing in so large a project," id. at 558, 68 S.Ct. 248. Here, there was no such evidence that Holck and Umbrell should have known that the conspiracy involved parts beyond White and Kemp. Accordingly, given the absence of any evidence to the contrary, we agree with Holck and Umbrell that the government failed to prove that they were aware of the existence of the other spokes.
Second, we agree with Holck and Umbrell that their activities and those of the other spokes were neither interdependent nor mutually supportive. In evaluating interdependence, we consider how helpful one individual's contribution is to another's goals. See United States v. Macchia, 35 F.3d 662, 671 (2d Cir.1994) (describing inquiry as "the extent to which the success or failure of one conspiracy is independent of a corresponding success or failure by the other"). We reiterate that interdependence serves as "evidence of an agreement," Perez, 280 F.3d at 346; that is, it helps establish whether the alleged coconspirators are "all committed to the same set of objectives in a single conspiracy," United States v. Smith, 82 F.3d 1261, 1271 (3d Cir.1996).
Chain-shaped conspiracies present the classic examples of interdependence. For instance, in Perez, 280 F.3d at 347, we concluded that two drug sellers and a drug smuggler were interdependent, even though there was a middleman between them, because "[the dealers] depended on a scheme involving [the smuggler and the middleman] and the shipment from the Philippines to possess and distribute the illegal drug." See also United States v. Portela, 167 F.3d 687, 697 (1st Cir.1999) (explaining that "a single conspiracy [exists] if the continued health of the trafficking and distribution network necessarily depends on the continued efforts of multiple suppliers"); United States v. Evans, 970 F.2d 663, 670 (10th Cir.1992) ("Interdependence is present when each alleged coconspirator . . . depend[s] on the operation of each link in the chain to achieve the common goal." (alterations in original) (internal quotation marks omitted)).[19]
*290 We also concluded that there was a single conspiracy in United States v. Kenny, 462 F.2d 1205 (3d Cir.1972), a non-drug case. Kenny involved a large-scale scheme that required contractors to pay kickbacks to government officials in order to procure government contracts. Id. at 1217. While the scheme involved a diverse group of individuals, the evidence showed "a determined group who repeatedly cooperated closely to achieve the common purpose of self-enrichment by extracting kickbacks." Id. Moreover, "[t]he key to success of all their depravities was their common control over the administration of city and county government." Id.; see also United States v. Greenidge, 495 F.3d 85 (3d Cir.2007) (finding single conspiracy where depositors of stolen and altered checks "did not represent independent customers, but were an integral part of this [pyramidal] `corporate' structure").
On the other hand, in Smith, we concluded that there was no interdependence between two kickback schemes because "[t]he co-conspirators in each state derived no benefit, financial or otherwise, from Smith's activities in the other state, nor was the success of the conspiracy in one state contingent on the success of the conspiracy in the other." 82 F.3d at 1271. Similarly, in United States v. Camiel, 689 F.2d 31 (3d Cir.1982), we found that the government had failed to prove a common, unified scheme between the officials of both houses of the Pennsylvania General Assembly in offering "no-show" patronage positions, because while each body did offer such positions, "there was a dearth of evidence presented that could link the relevant activities of the two legislative bodies." Id. at 37; see also Chandler, 388 F.3d at 811-12 ("In this case, there was no such interdependence of the spokes. The combined efforts of the spokes were not required to insure the success of the venture. No spoke depended upon, was aided by, or had any interest in the success of the others. Each spoke acted independently and was an end unto itself. The actions of one spoke did not facilitate the endeavors of other coconspirators or the venture as a whole." (footnote omitted)).
Based on these principles, we conclude that there was an insufficient degree of interdependence between Knight and Holck and Umbrell. While White and Kemp steered business to Knight's company RPC, this did not benefit Holck and Umbrell; it only benefitted Knight (and perhaps White). Nor did this arrangement cement White's hold on Kemp; if anything, it indebted White to Kemp, which again was of no use to Holck and Umbrell. Thus, it is difficult to conceive of how Knight's activities and those of Holck and Umbrell were interdependent or mutually supportive.
Hawkins's case is somewhat closer, because it is at least arguable that Hawkins's assistance to White in tendering bribes to Kemp inadvertently benefitted Holck and Umbrell by increasing White's power over Kemp. Nevertheless, we conclude that this degree of interdependency is too attenuated and incidental to establish that Holck and Umbrell and Hawkins joined the same conspiracy. The evidence here, as in Kotteakos and Smith, demonstrates that Holck and Umbrell's transactions were able to proceed without any reliance on Hawkins, and vice versa. Holck and Umbrell, through cultivating a relationship with White and providing loans to Kemp, induced Kemp to grant them favorable treatment. Hawkins also sought favors *291 from Kemp, and worked with White to coax those favors. Neither of these sets of transactions was contingent upon the other. Accordingly, we conclude that Holck and Umbrell and Hawkins were not interdependent.
The government's other arguments lack merit. For instance, the government claims that the conspirators overlapped because "White and Kemp, the core conspirators, dealt with every one of the coconspirators, including Holck and Umbrell, both individually and together." However, this could be said for any hub-and-spokes style conspiracy; Kotteakos and its progeny make clear that there must be overlap among the spokes, not just between the hub and the various spokes. Further, it is of no moment that the hub of this conspiracy involved two individuals instead of one. Smith recognized that the inquiry must focus not on the number of individuals who make up the hub, but on the character of the agreements between the spokes. See 82 F.3d at 1272. Thus, we conclude that appellants are correct that there was a variance between the conduct charged and proved.

2. Substantial Prejudice
We will only vacate Holck's and Umbrell's convictions, however, if they can show that the variance prejudiced their substantial rights. See United States v. Padilla, 982 F.2d 110, 115 (3d Cir.1992) (stating "assuming arguendo that Padilla has demonstrated a variance, he must also show prejudice to a substantial right"); Perez, 280 F.3d at 345 (same). The rule against variances serves at least three purposes. These purposes also illustrate why this rule contains a prejudice requirement. First, "the rule protects the right of each defendant `not to be tried en masse for the conglomeration of distinct and separate offenses committed by others.'" United States v. Schurr, 775 F.2d 549, 553 (3d Cir.1985) (quoting Kotteakos, 328 U.S. at 775, 66 S.Ct. 1239). The idea here is that the jury should not be permitted to transfer "`guilt from one alleged co-schemer to another.'" Perez, 280 F.3d at 346 (quoting United States v. Barr, 963 F.2d 641, 648 (3d Cir.1992)). Closely related to guilt transference is the possibility of evidence spillover. United States v. Trainor, 477 F.3d 24, 36 n. 21 (1st Cir.2007) (stating that "the spillover concern is addressed to whether incriminating evidence against co-defendants who were involved in separate conspiracies affected the jury's consideration of the evidence against the defendant"). Second, the rule ensures that a defendant has adequate notice of the charges being brought against him. Perez, 280 F.3d at 345. Third, the rule "rests on a principle akin to double jeopardy, for the rule helps to minimize the danger that the defendant may be prosecuted a second time for the same offense." Schurr, 775 F.2d at 554 (internal quotation marks omitted). The third purpose is not at issue in this case, and the "notice" purpose has not been violated because Holck and Umbrell were aware from the indictment as to their role in the conspiracy, even if this conspiracy had been solely between them and the White/Kemp hub. There is no reasonable argument that Holck and Umbrell were not aware of the nature of the charges brought against them.
Here, Holck and Umbrell have failed to show that the variance prejudiced their substantial rights. They argue that they were prejudiced because a great deal of evidence concerning "seamy explicit . . . quid pro quo trades" between White and Kemp were introduced against them. According to Holck and Umbrell, "these damning conversations had nothing to do with [them]." However, as the government notes, this evidence was admissible *292 against Holck and Umbrell because, as they concede, they joined a conspiracy with White and Kemp. See, e.g., United States v. Kushner, 305 F.3d 194, 198 (3d Cir.2002) (explaining that "[u]nder the law of conspiracy, a defendant is liable for his own and his co-conspirators' acts for as long as the conspiracy continues"). This conspiracy involved White's bribing Kemp in order to control his decision-making and direct city business to favored companies  including Commerce. Thus, evidence concerning White and Kemp's relationship was relevant to Holck and Umbrell to explain White's power over Kemp, which worked in Holck and Umbrell's favor. Accordingly, Holck and Umbrell's argument on this point lacks merit.
Further, as the government explains, it rigorously segmented its proofs and "never suggested in any way that any piece of evidence related to Hawkins and Knight was relevant to establish Holck and Umbrell's participation in the conspiracy." This Court has specifically found, in a discussion of variance, no prejudice because, inter alia, "the presentation against the defendants here proceeded seriatim." Padilla, 982 F.2d at 116. We explained that the presentation of evidence in this manner minimized the risk of evidence spillover from the separate defendants. Id.; see also Perez, 280 F.3d at 347; Greenidge, 495 F.3d 85. The same rationale applies here.
Also militating against a finding of prejudice is Kotteakos's explanation that the danger of prejudice increases along with the number of conspiracies and individuals that make up the wrongly charged single conspiracy. As the Court stated, "[o]bviously the burden of defense to a defendant, connected with one or a few of so many distinct transactions, is vastly different not only in preparation for trial, but also in looking out for and securing safeguard against evidence affecting other defendants." Id. at 766-67, 66 S.Ct. 1239. The Court distinguished the conspiracy in that case, which involved eight different conspiracies encompassing between 13 and 32 individuals and did prejudice the defendant, from the case of Berger v. United States, 295 U.S. 78, 55 S.Ct. 629, 79 L.Ed. 1314 (1935), where two conspiracies involving four individuals were proved and did not prejudice the defendant. Id. at 766, 66 S.Ct. 1239. This case is more similar to Berger, as there were five alleged conspirators that make up three distinct conspiracies. Thus, there is little danger that prejudice inevitably occurred based on the sheer number of defendants and conspiracies.
Accordingly, while Holck and Umbrell have shown that there was a variance between the charge in the indictment and the evidence adduced at trial, they have failed to demonstrate that they were prejudiced by the variance.
D. Hawkins's Wire Fraud Conviction
La-Van Hawkins challenges the sufficiency of the evidence supporting his conviction for aiding and abetting wire fraud, which related to his transmitting the second $5,000 to Kemp. Hawkins argues that there may have been sufficient evidence to show that he intended to aid and abet some sort of criminal activity, but that the government failed to present evidence demonstrating that he intended to aid and abet the specific crime of honest services fraud. Again, we will "view the evidence in the light most favorable to the Government and sustain the verdict if any rational juror could have found the elements of the crime beyond a reasonable doubt." Cartwright, 359 F.3d at 286 (internal quotation marks omitted).
*293 Hawkins's argument is based on the general precept that in order to convict a defendant of aiding and abetting, the government must prove that "the defendant charged with aiding and abetting that crime knew of the commission of the substantive offense and acted with the intent to facilitate it." United States v. Dixon, 658 F.2d 181, 189 n. 17 (3d Cir.1981). We applied this principle in United States v. Wexler, 838 F.2d 88 (3d Cir.1988), where we held that the government had presented insufficient evidence to sustain the defendant's conviction for aiding and abetting possession by others with intent to distribute hashish. Id. at 90. While the government had presented evidence that would have allowed a jury to find that the defendant was involved in an operation with two other men that involved transporting cargo in a truck, that the defendant served as a lookout as the other defendants moved the truck, and that the truck was loaded with hashish, id. at 91, we concluded that the government had failed to present enough evidence that the defendant knew that the truck held drugs, id. at 92. We explained that because the government had failed to show that the defendant "had knowledge of the hashish," it failed to prove that the defendant purposely aided and abetted the specific crime with which he was charged. Id. We concluded that the evidence presented was just as consistent with the crime of transporting stolen goods  an entirely different crime. Id.
In the instant case, however, the government presented sufficient evidence for the jury to conclude that Hawkins intended to aid and abet honest services fraud. The government demonstrated that Hawkins knew that Kemp held public office in Philadelphia and that Hawkins knew that White was a politically connected Philadelphia lawyer. Moreover, the government showed that Hawkins had no reason to provide money to Kemp, and that he actually relayed the money to Kemp at White's behest after White provided him with a $5,000 check. The government also presented evidence that Hawkins filled out the entire check except for the payee line, although he did intend for the money to go to Kemp, as demonstrated by the subsequent wire transfer. This evidence all supports the jury's conclusion that Hawkins intended to aid and abet White's corruption of Kemp. Hawkins argues that this situation is just as consistent with drug conspiracy, money laundering, or tax fraud; however, the government's theory specifically accounts for Kemp's position as a public official in a way that Hawkins's other proposed crimes do not, which differentiates this case from Wexler. As we have explained, "[t]here is no requirement . . . that the inference drawn by the jury be the only inference possible or that the government's evidence foreclose every possible innocent explanation." United States v. Iafelice, 978 F.2d 92, 97 n. 3 (3d Cir. 1992). Thus, we reject Hawkins's argument and will affirm his conviction for aiding and abetting honest services wire fraud.
E. Hawkins's Perjury Convictions
Hawkins next challenges the sufficiency of the evidence undergirding his three perjury convictions under 18 U.S.C. § 1623, which prohibits "knowingly mak[ing] any false material declaration" under oath before a grand jury. For each perjury conviction, Hawkins contends that the government failed to prove that his relevant testimony before the grand jury was untrue. We will uphold the verdict if a reasonable jury could have found the elements of the crime beyond a reasonable doubt. Dent, 149 F.3d at 187. The government may prove guilt "via circumstantial evidence." United States v. Serafini, 233 F.3d 758, 770 (3d Cir.2000); see *294 also 18 U.S.C. § 1623(e) ("Proof beyond a reasonable doubt under this section is sufficient for conviction. It shall not be necessary that such proof be made by any particular number of witnesses or by documentary or other type of evidence."); United States v. Smith, 538 F.2d 159, 163 (7th Cir.1976) ("Although no direct evidence of perjury was produced, none was required.").
We first reject Hawkins's argument that the government presented insufficient evidence to prove the falsity of his testimony that he provided the first $5,000 check to Kemp as a wedding present on White's instructions. As the government argued, the story that Hawkins presented is unlikely on its face: it is difficult to understand why Hawkins would agree to give a $5,000 wedding gift to someone he barely knew. Further, the government presented evidence that Kemp had already been married for 20 months by the time that Hawkins wrote this check. While it is true, as Hawkins responds, that that could mean only that White lied to Hawkins, it nevertheless places Hawkins's account in further doubt. Additionally, and vitally, the government demonstrated that Hawkins testified falsely about the details surrounding this payment. According to Hawkins's grand jury testimony, White and Kemp were in Detroit for Kemp's bachelor party, and during that trip, dropped by Hawkins's office. While there, Hawkins testified, White asked Hawkins to give Kemp a check as a wedding present. However, the government showed that Kemp was not actually in Detroit at the time. This contradiction could have allowed the jury to draw two inferences. First, the jury could have concluded that Hawkins lied when he said that Kemp's bachelor party was occurring, which makes the wedding present explanation less plausible. Second, if Kemp was not in Detroit at all, it would be extremely unlikely that White would request a wedding present for him. Moreover, while Hawkins testified that the check was never cashed, it was. We conclude that this series of contradictions and implausibilities are sufficient to sustain the jury's verdict on this count.
We are similarly unpersuaded by Hawkins's argument that the government failed to prove the falsity of his grand jury testimony in which he stated that he supplied the second $5,000 check to White intending for White to convey it to a coalition of African-American newspapers. Most damaging to Hawkins's testimony is the fact that after this check bounced twice, Hawkins wired the $5,000 directly to Kemp's bank account. This is powerful evidence that Hawkins intended for the $5,000 to reach Kemp  not a newspaper association. While this fact alone is sufficient to sustain the conviction, we also note that the details that Hawkins provided further undermine the veracity of the story. For instance, the government demonstrated that Hawkins had met with the group two years before writing the check, making his sudden beneficence unusual. Thus, we will affirm the jury's verdict on this count.
We also make short shrift of Hawkins's claim that the government proffered insufficient evidence to prove the falsity of his testimony regarding his meeting with Khan, in which he stated that he had not specifically asked White to bring Kemp to the meeting, although he had asked, on behalf of Khan, for the attendance of someone who could discuss property opportunities in Philadelphia. Hawkins's testimony is flatly contradicted by the recorded telephone conversation in which Hawkins specifically asked White to bring "Corey" to the meeting in order to "keep [Khan] in the hole" by convincing Khan *295 that Hawkins was "gonna be gettin' 20 million." Moreover, Khan testified that he never intended to enter the Philadelphia market and did not ask Hawkins to introduce him to anyone. This evidence was plainly sufficient to permit the jury to conclude that Hawkins's grand jury testimony was false on this matter.
F. Hawkins's Evidentiary Challenges
Hawkins next challenges a string of the District Court's evidentiary rulings. First, he argues that the evidence the government presented that mentioned Al Sharpton should have been excluded. For instance, in the government's opening statement it stated:
Where is a source of money? La-Van Hawkins is looking for big public pension funds, and to get access to the money in big public pension funds Mr. Hawkins knows you need to have access to public officials. You will hear that is exactly what La-Van Hawkins tries to do. He tries to do it through Reverend Al Sharpton in the city of New York. In Philadelphia, he tries to do it through Ron White. . . .
(App. at 1527.) Hawkins argues that this and all subsequent references to Sharpton were irrelevant and thus inadmissible under Fed.R.Evid. 401. Alternatively, Hawkins argues that the evidence should have been excluded under Fed.R.Evid. 403 because any probative value that the evidence did have was "substantially outweighed by the danger of unfair prejudice." "We review a district court's decision to admit or exclude evidence for abuse of discretion, and such discretion is construed especially broadly in the context of Rule 403." United States v. Mathis, 264 F.3d 321, 326-27 (3d Cir. 2001).
Contrary to Hawkins's assertion, the evidence involving Sharpton did have a "tendency to make the existence of any fact that is of consequence to the determination of the action more probable or less probable than it would be without the evidence." Fed.R.Evid. 401. As we have recognized, this standard is "not high." United States v. Steele, 685 F.2d 793, 808 (3d Cir.1982) (internal quotation marks omitted). At bottom, the government aimed to prove that Hawkins joined a conspiracy to corrupt Kemp. The evidence concerning Hawkins's efforts to cultivate a relationship with Sharpton emphasized Hawkins's interest in fostering ties with politically active individuals, and was thus probative as to Hawkins's intent in working with White and directing money to Kemp. The evidence could have allowed a jury to conclude that it was less likely that the first payment to Kemp was casually made at White's direction, that the second payment was not intended for Kemp at all, and that Hawkins was generally indifferent toward Kemp's position, because the evidence concerning Sharpton helped show just how determinedly Hawkins wooed those with political connections and his willingness to convey money to them. Of course, this evidence alone does not prove Hawkins's guilt on any count, but as the notes to Rule 401 explain, "a brick is not a wall." Fed. R.Evid. 401 advisory committee's note (internal quotation marks omitted).
Moreover, Hawkins has failed to present any authority for his novel position that Sharpton's name alone is so prejudicial that the infrequent references to it substantially outstripped the probative value of this evidence. Further, the District Court minimized the possibility of prejudice by explicitly instructing the jury that: "The government is not alleging anything wrong at all regarding the efforts of La-Van Hawkins, Ronald White, and Al Sharpton concerning New York pension funds. There is no suggestion of illegality *296 as to any recorded conversations you heard played during the government's case-in-chief pertaining to Al Sharpton. . . ." (App. at 10593-94.) Accordingly, we conclude that the District Court did not abuse its discretion in admitting the evidence under either Rule 401 or 403.
Second, Hawkins argues that the testimony of representatives of Blockbuster, BET, Pizza Hut, and Burger King, all of whom contradicted claims that Hawkins made before the grand jury about his great wealth,[20] should have been excluded under Rule 404(b). In order to be admissible under Fed.R.Evid. 404(b), the evidence of other acts must: "(1) have a proper evidentiary purpose, (2) be relevant under Rule 402, (3) satisfy Rule 403 (i.e., not be substantially more prejudicial than probative), and (4) be accompanied by a limiting instruction, when requested pursuant to Federal Rule of Evidence 105, that instructs the jury not to use the evidence for an improper purpose." United States v. Cross, 308 F.3d 308, 320-21 (3d Cir. 2002) (footnote omitted). Hawkins argues that this evidence was offered for an improper purpose and that its probative value was substantially outweighed by the danger of unfair prejudice. We review the District Court's judgments for abuse of discretion. United States v. Mastrangelo, 172 F.3d 288, 295 (3d Cir.1999). As explained below, we conclude that the District Court acted within its discretion.
Hawkins first argues that this evidence was not presented for a proper purpose, because it was offered to persuade the jury that because Hawkins had lied to the grand jury on other occasions, he must have been guilty of the perjury charges. To show a proper purpose, "the government must `clearly articulate how that evidence fits into a chain of logical inferences' without adverting to a mere propensity to commit crime now based on the commission of crime then." Id. (quoting United States v. Sampson, 980 F.2d 883, 887 (3d Cir.1992)).
We are unpersuaded by Hawkins's argument on this point. The government argues that it introduced this evidence to demonstrate Hawkins's consciousness of his guilt of the underlying charges, which we have recognized is a proper purpose under Rule 404(b). See United States v. Gatto, 995 F.2d 449, 455 (3d Cir.1993) (explaining that testimony was "admissible under Rule 404(b) . . . to show consciousness of guilt"); see also United States v. Rajewski, 526 F.2d 149, 158 (7th Cir.1975) ("It is well-settled that untrue exculpatory statements may be considered as circumstantial evidence of the defendant's consciousness of guilt."). Throughout Hawkins's grand jury testimony, Hawkins defended his conduct essentially by arguing that he was too wealthy to deign to involve himself in the paltry corruption alleged in the case. For instance, after being asked whether Hawkins was concerned that providing *297 money to Kemp constituted money laundering, Hawkins responded: "Well, no ma`am, for the simple reason money laundering is  first of all, because I had businesses all my money came from. I made all my money from legitimate sources. As a matter of fact I sold Checkers for 50 million dollars and returned Burger King for 35 million dollars. So I've never had any reason to launder money." (App. at 14815.) This response is illustrative of the general tenor of Hawkins's grand jury testimony, in which he sought to equate wealth with innocence.[21] Thus, the government's evidence disproving these claims of vast wealth effectively impeached what Hawkins presented as an (unusual form of) alibi.
We also agree with the government that the District Court did not abuse its discretion in determining that the evidence was admissible under Rule 403. See United States v. Jemal, 26 F.3d 1267, 1272 (3d Cir.1994) ("If judicial self-restraint is ever desirable, it is when a Rule 403 analysis of a trial court is reviewed by an appellate tribunal." (internal quotation marks omitted)). Given that we have frequently approved district courts' decisions to admit previous drug convictions against defendants in subsequent drug prosecutions, see Sampson, 980 F.2d at 887 ("There is no question that, given a proper purpose and reasoning, drug convictions are admissible in a trial where the defendant is charged with a drug offense."), it cannot be, as Hawkins argues, that the similarity between his other conduct and charged conduct necessarily causes unfair prejudice. Because evidence of Hawkins's consciousness of guilt was of high probative value to the government's case, Hawkins faces a high hurdle in showing that the danger of unfair prejudice substantially outweighed the probative value. See Cross, 308 F.3d at 325 ("`Rule 403 . . . does not generally require the government to sanitize its case, to deflate its witnesses' testimony, or to tell its story in a monotone.'") (quoting United States v. Gartmon, 146 F.3d 1015, 1021 (D.C.Cir.1998)). While Hawkins attempts to surmount this hurdle by arguing that the government presented this evidence to convince the jury that Hawkins had committed crimes because of financial distress, we are not persuaded. See, e.g., United States ex rel. Mertz v. State of N.J., 423 F.2d 537, 541-42 (3d Cir.1970) (recognizing this danger). There is a substantial difference between financial distress and not reaping huge profits from transactions, and the District Court took care to protect Hawkins from the evidence of the former by rejecting the government's attempt to impeach Hawkins's statement that he was a multi-millionaire.[22] We thus conclude that the District Court did not abuse its discretion in determining *298 that the evidence was admissible under Rules 403 and 404.[23]
Next, Hawkins argues that the District Court erred by admitting a letter found in Kemp's home as a co-conspirator statement under Fed.R.Evid. 801(d)(2)(E). The letter, which was dated March 20, 2002, and was addressed from Kemp to Hawkins, stated: "Let me take this opportunity to thank you for selecting me to serve in the capacity of a financial consultant for your company. I look forward to working and sharing my expertise with you in the very near future. Please feel free to contact me at your convenience." (App. at 13944.) In order to admit a statement under Rule 801(d)(2)(E), a district court must find, by a preponderance of the evidence: "(1) that a conspiracy existed; (2) the declarant and the party against whom the statement is offered were members of the conspiracy; (3) the statement was made in the course of the conspiracy; and (4) the statement was made in furtherance of the conspiracy." United States v. McGlory, 968 F.2d 309, 333 (3d Cir.1992). We exercise plenary review over these findings. Id.
We agree with the District Court that this letter was admissible against Hawkins as the statement of an alleged coconspirator. While Hawkins argues that the government failed to present any evidence besides this letter demonstrating that Hawkins and Kemp were members of a conspiracy, that is simply not true: just ten days before Kemp wrote this letter, he had accepted a $5,000 check from Hawkins. The transfer of money from Hawkins to Kemp could certainly have formed part of the alleged conspiracy. It does not matter whether or not Kemp actually mailed the letter to Hawkins, because its mere existence provided evidence that Kemp knew of the inappropriate nature of the $5,000 check from Hawkins. Accordingly, we will affirm the District Court's admission of the letter.
Finally, Hawkins argues that the District Court erred by admitting evidence *299 concerning Kemp's actual wedding date, arguing that this evidence is inadmissible under Rules 401 and 403. According to Hawkins, this evidence was irrelevant because he testified before the grand jury only that White told him that Kemp's wedding had recently occurred, not that it actually had. As noted, "[w]e review a district court's decision to admit or exclude evidence for abuse of discretion, and such discretion is construed especially broadly in the context of Rule 403." Mathis, 264 F.3d at 326-27.
Again, we conclude that the District Court acted within its discretion in admitting this evidence. As we have noted, Rule 401 does not set a high standard. See Steele, 685 F.2d at 808; see also Sampson, 980 F.2d at 888 (stating that "the burden [on the proponent of the evidence] is not onerous"). Just as evidence that Kemp had recently been married would have made it more probable that White had actually made this statement to Hawkins, the fact that Kemp had been married so long ago made it less probable. Moreover, Hawkins has failed to explain why this evidence was unfairly prejudicial to him. He was free to present his explanation that notwithstanding the date of Kemp's actual marriage, White had said that the $5,000 was for a wedding present, and he did so in his closing argument. Accordingly, we perceive no reason to conclude that the District Court abused its "very substantial discretion" in admitting this evidence. United States v. Ali, 493 F.3d 387 (3d Cir.2007) (internal quotation marks omitted).
G. Hawkins's Jury Instructions Challenge
Hawkins also challenges the jury instructions regarding his conviction for aiding and abetting wire fraud, arguing that the District Court failed to explain to the jury that it was required to find Hawkins's culpable participation in the specific scheme charged in the indictment. Because Hawkins did not raise this challenge until after the close of trial, we review for plain error. Fed.R.Crim.P. 30(d). Under the plain error standard, we will reverse the District Court only upon finding "(1) an error; (2) that is plain; and (3) that affected substantial rights." United States v. Dobson, 419 F.3d 231, 236 (3d Cir.2005). Here, we find no error.
Hawkins argues that the jury instructions failed to conform to Dobson's requirement that the defendant culpably participate in the illicit enterprise charged in the indictment. Id. at 237. In Dobson, the defendant, Dobson, was charged with mail fraud (among other things). Id. at 234. Dobson had worked as a salesperson for Universal Liquidators (UL), which claimed to be in the business of locating and reselling surplus merchandise. Id. Dobson's role was to convince individuals to pay approximately $5,000 to UL for access to this merchandise, which the individuals could then sell to the public at a profit. Id. However, UL was a hoax  it was not actually able to connect individuals with deeply discounted merchandise. Id. Further, Dobson, while marketing this "opportunity," made misrepresentations of her own, such as claiming that by selling merchandise acquired through UL she had made enough money to purchase a horse ranch. Id. at 235.
We found that the District Court had committed plain error because its jury instructions failed to "require [] a determination of whether Dobson knowingly participated in UL's broader scheme to defraud." Id. at 238. The instructions merely called upon the jury to determine "whether the defendant knowingly devised or participated in a scheme to defraud." Id. (emphasis added). We explained *300 that the "case present[ed] two layers of potential fraud or misrepresentation that do not necessarily interconnect: (1) Dobson's dubious sales presentations; and (2) the fraudulent UL scheme charged in the Indictment." Id. While only the second kind of fraud was charged in the indictment, the jury instructions permitted the jury to convict upon finding either kind. Id. Accordingly, we held that the instructions had "omitted the prosecution's obligation to show that Dobson knowingly devised or participated in the broader UL scheme as charged in the Indictment." Id.
At bottom, Dobson simply ensures that the jury instructions require the jury to find that the defendant culpably participated in the particular "illicit enterprise" that was charged in the indictment. Id. at 237. We have no doubt that the jury instructions in this case did so. The indictment charged Hawkins with aiding and abetting honest services wire fraud. Accordingly, the relevant scheme was the "scheme to defraud the City of Philadelphia and its citizens of the right to defendant COREY KEMP's honest services." (App. at 581.) The District Court defined honest services fraud extensively, and then referred the jurors to the verdict sheet, which, as relevant here, charged Hawkins with aiding and abetting honest services wire fraud. The Court explained that:
[O]nly a public official owes a duty of honest services to the people he serves. Thus, of the defendants in this case, only Kemp is a public official. Each of the other defendants, who are private citizens, by himself or herself may not commit a substantive offense of honest services fraud as charged in the indictment.
However, you may nevertheless find one or more of the other defendants guilty of honest services fraud, if you find beyond a reasonable doubt that such a defendant aided and abetted; that is, assisted a public official who was committing this crime to commit this crime.
(App. at 9652.)
The District Court went on to instruct the jury that: Before a defendant may be held responsible for aiding and abetting others in the commission of a crime, it is necessary that the government prove beyond a reasonable doubt that the defendant knowingly and deliberately associated himself or herself in some way with the crime charged and participated in it with the intent to commit the crime.
In order to be found guilty of aiding and abetting the commission of a crime, the government must prove beyond a reasonable doubt that the defendant:
First, knew that the crime charged was to be committed or was being committed.
Second, knowingly did some act for the purpose of aiding the commission of that crime.
And third, acted with the intention of causing the crime charged to be committed.
(App. at 9653.)
These instructions contained the direct link between Hawkins's actions and the specific scheme that was charged in the indictment  the scheme to deprive the public of Kemp's honest services  that was lacking in Dobson. The instructions left no danger that Hawkins would be convicted for aiding and abetting some other scheme. Accordingly, we conclude that the instructions are consistent with Dobson's teaching, and we reject Hawkins's argument.


*301 H. District Court's Questioning the Jury and Discharging Juror 11

1. Individual Questioning
All appellants argue vigorously that the District Court should not have questioned the jurors about Juror 11's alleged misconduct. We review "a trial court's response to allegations of juror misconduct for abuse of discretion." United States v. Boone, 458 F.3d 321, 326 (3d Cir.2006). Here, we conclude that the District Court acted within its discretion when it individually questioned the jurors.
We have recently had occasion to set forth the applicable legal standard governing the district courts' latitude to question jurors during deliberations about allegations of misconduct. In Boone, we recognized that "[i]t is beyond question that the secrecy of deliberations is critical to the success of the jury system." Id. at 329. At the same time, we emphasized that "[i]t is also manifest, however, that a juror who refuses to deliberate or who commits jury nullification violates the sworn jury oath and prevents the jury from fulfilling its constitutional role." Id. Attempting to reconcile these disparate values, we held that "where substantial evidence of jury misconduct  including credible allegations of jury nullification or of a refusal to deliberate  arises during deliberations, a district court may, within its sound discretion, investigate the allegations through juror questioning or other appropriate means." Id. We stressed that a district court, "based on its unique perspective at the scene, is in a far superior position than this Court to appropriately consider allegations of juror misconduct, both during trial and during deliberations." Id.
Applying that legal principle in Boone, we affirmed the District Court's decision to question a juror after the Court received a note stating:
We have some serious concern about one of our fellow jurors. He has told . . . all of us several times that his best friend is a cop, and he has several guns, some unregistered and being stored at his friend's house. This leads us to believe that he lied on his initial questionnaire for jury selection. Also, he refuses to discuss certain [counts] because he had his mind made up before we started deliberating. He has said he does not believe anything the police said and thinks everyone is lying. We feel this seriously affects our deliberations. Our votes are 11 to [] 1 on four [counts] and we have agreed on four. The juror in question has stated they will not change their mind [sic] and does not want to work at any evidence or discuss any testimony. We seem to be at an impasse. Please help us. Thank you, [jury foreperson].
Id. at 324 (alterations in original). The appellant argued that this note presented insufficient justification for the District Court to question the juror. We rejected that argument, explaining that "[a]lthough this evidence was far from unambiguous, there was a sufficient indication that Juror X was violating his oath to provide discretion to the trial judge to investigate further." Id. at 330.
Accordingly, the legal standard is clear: a district court may investigate allegations of juror misconduct when presented with "substantial evidence" of that misconduct. All appellants protest that the District Court here was not presented with substantial evidence of misconduct.
The first individualized investigation was precipitated by two notes: one accused a juror of being biased, while another accused a juror of refusing to consider evidence and deliberate. This evidence is at least as strong as that presented in Boone, *302 and, recognizing that the District Court was in the best position to understand and respond to the exigencies of the situation, we conclude that those notes amounted to "substantial evidence of jury misconduct."
The District Court's second voir dire was also an acceptable use of its discretion. It is true that the note that prompted this investigation was ambiguous: a court could have read the note either to state that further deliberations would be useless because the jurors simply could not agree or because one juror was violating her oath by failing to participate. While the note alone may have been insufficient to justify questioning the jurors a second time, the District Court was not operating from a blank slate. The District Court had previously fielded complaints from jurors  both by note and during the first questioning  that Juror 11 was failing to deliberate. Thus, the District Court certainly could have interpreted this note to allege further misconduct, which, taken in tandem with previous allegations, was sufficient to permit the District Court to exercise its discretion to investigate further. See Boone, 458 F.3d at 330 (stating that "[t]he fact that a different judge may have chosen not to conduct a[n] investigation is irrelevant"). Accordingly, we conclude that the District Court acted within its discretion in choosing to conduct a second session of individual questioning.
Finally, the third investigation was also appropriate. This series of questioning was prompted by the District Court's receiving two notes: the first claimed that a juror was biased, and the second exhorted the judge to question the jurors. A specific allegation of bias, made after the District Court had exhaustively instructed the jurors on proper and improper bias, provided substantial evidence of juror misconduct.
While it may be more intrusive to question each juror individually, as occurred here, than only the subject of the allegation of misconduct, as occurred in Boone, we nevertheless conclude that the District Court acted well within its discretion when it used the more-expansive mode of investigation. We have recognized that there are times in which individual questioning is the optimal way in which to root out misconduct, see United States v. Resko, 3 F.3d 684, 686 (3d Cir.1993) (holding that district court's use of questionnaire, instead of, for instance, individualized voir dire, was "inadequate to enable the court to fulfill its responsibility of providing an appropriate cautionary instruction and of determining whether prejudice resulted from the jury misconduct"); United States v. Console, 13 F.3d 641, 667 (3d Cir.1993) (calling individual voir dire the "method of inquiry [that] we have preferred"), and that the District Court must utilize procedures that will "provide a reasonable assurance for the discovery of prejudice," Martin v. Warden, Huntingdon State Corr. Inst., 653 F.2d 799, 807 (3d Cir.1981). Crucially, the District Court took care to limit its questions to appropriate matters that did not touch on the merits of the jury's deliberation, and expressly informed each juror on multiple occasions that he or she should not reveal the substance of the deliberations. See United States v. Edwards, 303 F.3d 606, 634 n. 16 (5th Cir.2002) (explaining that "the district court was very careful; it insisted that the jurors refrain from describing the content and method of their deliberations"). As we have recognized, the District Court was in the best position to evaluate what kind of investigation the circumstances demanded, see Boone, 458 F.3d at 329; here, its decision was reasonable. Accordingly, we conclude that the District Court acted within its discretion to question the jurors on all three occasions.


*303 2. Discharging Juror 11
All appellants also assert that the District Court erred by dismissing Juror 11. We review the dismissal of a juror for cause for abuse of discretion. See United States v. Gambino, 788 F.2d 938, 949 (3d Cir.1986). Here, the District Court acted within its discretion in discharging Juror 11.
While it is undisputed that in certain circumstances, district courts may discharge a juror for cause during deliberations, see Fed.R.Crim.P. 23(b), we have yet to enunciate the appropriate standard.[24] Any standard must accommodate two clashing interests. First, it is clear that "a court may not dismiss a juror during deliberations if the request for discharge stems from doubts the juror harbors about the sufficiency of the government's evidence." United States v. Brown, 823 F.2d 591, 596 (D.C.Cir.1987). Any other rule would eviscerate the right to a unanimous verdict of guilt. See id. On the other hand, courts agree that a district court has the authority to dismiss a juror  even during deliberations  if "that juror refuses to apply the law or to follow the court's instructions." United States v. Abbell, 271 F.3d 1286, 1302 (11th Cir.2001) (per curiam). That is because "a juror who refuses to deliberate or who commits jury nullification violates the sworn jury oath and prevents the jury from fulfilling its constitutional role." Boone, 458 F.3d at 329. While the jurisprudence discussing the discharge of jurors during deliberations has largely focused on a refusal to deliberate or jury nullification, its reasoning applies with equal force to claims of juror bias.[25]Cf. Gov't of V.I. v. Dowling, 814 F.2d 134, 139 (3d Cir.1987) ("The trial court's finding [of whether a juror is biased] is a finding of `historical fact: did a juror swear that he could set aside any opinion he might hold and decide the case on the evidence, and should the juror's protestation of impartiality have been believed.'") (quoting Patton v. Yount, 467 U.S. 1025, 1036, 104 S.Ct. 2885, 81 L.Ed.2d 847 (1984)).
Because of the danger that a juror will be discharged based on that juror's view of the evidence, courts "apply a tough legal standard." Abbell, 271 F.3d at 1302. In Brown, for instance, the D.C. Circuit held that "if the record evidence discloses any possibility that the request to discharge stems from the juror's view of the sufficiency of the government's evidence, the court must deny the request." 823 F.2d at 596. Similarly, in United States v. Thomas, 116 F.3d 606 (2d Cir.1997), the Second Circuit adopted the "any possibility" standard set forth in Brown. Id. at 622.
Subsequently, however, courts have slightly modified that language. The Ninth Circuit has held that "if the record evidence discloses any reasonable possibility that the impetus for a juror's dismissal stems from the juror's views on the merits of the case, the court must not dismiss the juror." United States v. Symington, 195 F.3d 1080, 1087 (9th Cir. 1999). The court determined that it was necessary to include the word "reasonable," given that "[i]t may be that `[a]nything *304 is possible in a world of quantum mechanics.'" Id. at 1087 n. 5 (second alteration in original) (quoting United States v. Watkins, 983 F.2d 1413, 1424 (7th Cir.1993) (Easterbrook, J., dissenting)). Similarly, in Abbell, the Eleventh Circuit held that "a juror should be excused only when no `substantial possibility' exists that she is basing her decision on the sufficiency of the evidence." 271 F.3d at 1302. The court explained that it meant for the standard to "be basically a `beyond reasonable doubt' standard," that it intended district courts to apply the "substantial possibility" standard, and that it would then review the district courts' factual findings for clear error. Id. at 1302-03.
While there is a slight difference in the standards as expressed by the D.C. and Second Circuits as compared to the Ninth and Eleventh Circuits, we believe that the difference is one of clarification and not disagreement. To the extent that there is a difference, we believe that the articulation of the Ninth and Eleventh Circuits is superior. That standard will allow us to avoid abstract "anything is possible" arguments, provide district courts with some leeway in handling difficult juror issues, and protect each party's right to receive a verdict rendered by a jury that follows the law. At the same time, the standard is by no means lax: it corresponds with the burden for establishing guilt in a criminal trial, so we are confident that it will adequately ensure that jurors are not discharged simply because they are unimpressed by the evidence presented.[26] We adopt such a high standard in part because, as a result of our recent decision in Boone, a district court in the Third Circuit has more leeway to investigate juror misconduct than in other circuits. See, e.g., Symington, 195 F.3d at 1086; Thomas, 116 F.3d at 618-21; Brown, 823 F.2d at 596. Accordingly, we hold that the district courts may discharge a juror for bias, failure to deliberate, failure to follow the district court's instructions, or jury nullification when there is no reasonable possibility that the allegations of misconduct stem from the juror's view of the evidence.
Here, the evidence supporting the District Court's conclusion is overwhelming. The District Court carefully and correctly instructed the jurors on the distinction between permissible and impermissible bias, and during the final voir dire, ten jurors reported that Juror 11 *305 was improperly biased.[27] Significantly, the District Court ruled that Juror 11 was not credible, and we see no reason to upset that conclusion. See Kirk v. Raymark Indus., Inc., 61 F.3d 147, 153 (3d Cir.1995) (stressing that "the district court should not rely simply on the jurors' subjective assessments of their own impartiality"); Abbell, 271 F.3d at 1303 (stating that "because the demeanor of the pertinent juror is important to juror misconduct determinations, the district court is uniquely situated to make the credibility determinations that must be made in cases like this one: where a juror's motivations and intentions are at issue"). Even on the sterile record before us, the District Court's conclusion is inescapable. Based on what the other jurors reported, it is simply unbelievable that Juror 11 really stated that FBI agents were among the most credible witnesses. Such a statement is so inconsistent with all the other reports that it tends to prove the opposite: that Juror 11 was indeed biased and constructed a post hoc story to try to obfuscate that bias.
In addition to the refrain of allegations of bias, during the final voir dire eight jurors reported that Juror 11 was refusing to deliberate and ten jurors reported that Juror 11 was refusing to discuss the evidence. For instance, Juror 6, Juror 11's staunchest defender, reported that Juror 11 was deliberating and was not biased; however, even Juror 6 believed that Juror 11 was refusing to look at the evidence. A refusal to deliberate or discuss the evidence may well be a manifestation of underlying bias: if a juror makes up her mind based on beliefs formed before the trial began, she would have no reason to discuss the evidence with other jurors. Here, the vast majority of jurors concluded that Juror 11 acted inappropriately in those ways, too. We emphasize that the District Court removed Juror 11 because of her bias, and we therefore need not address whether the District Court would have abused its discretion if it removed Juror 11 on refusal to deliberate grounds rather than due to bias.
Given that the "reasonable possibility" test we have adopted is similar to the beyond-a-reasonable-doubt standard, analogizing this situation to a criminal proceeding is useful. We have little doubt that if ten or 11 out of 12 witnesses testified against a defendant, and the defendant testified in a patently unbelievable manner, the jury could find guilt beyond a reasonable doubt. Similarly, under the circumstances presented here, we conclude that the District Court appropriately exercised its discretion in concluding that there was no reasonable possibility that the allegations against Juror 11 were based on her view of the evidence.
Our decision comports with the leading cases to consider the discharge of a juror during deliberations. Those that reversed the District Court's decision to discharge involved much more equivocal evidence of misconduct. For instance, in Brown, upon questioning a juror who claimed that he was unable to perform his duty and apply the law, the juror revealed that he had a problem with "the way [the RICO statute was] written and the way the evidence has been presented," and that "[i]f the evidence *306 was presented in a fashion in which the law is written, then, maybe, I would be able to discharge my duties." 823 F.2d at 592-94. That response, which was uncontradicted on the record, clearly points to the juror's view of the evidence.
Similarly, in Thomas, the jurors presented varying explanations of the nature of their problem with the other juror. 116 F.3d at 623-24. Five jurors stated that the juror at issue was unyieldingly in favor of acquitting the defendants, either because the defendants were "his people," because the defendants were "good people," or because the defendants committed the crime out of economic necessity. Id. at 611. On the other hand, five jurors linked the juror at issue's reticence to convict to his views about the evidence  one juror stated that the juror was discussing the evidence, and four others stated that he had found the evidence insufficient or unreliable. Id. The true basis for the juror's feelings was thus unclear, and accordingly, the court concluded that the district court erred in discharging him. Id. at 624.
Meanwhile, in Abbell, the Eleventh Circuit affirmed the district court's decision to discharge a juror where the court explained that early on in the process the juror at issue had made comments about not having to follow the law, and even after the court gave corrective instructions, the majority of the other jurors still reported that the other juror would not consider the evidence or discuss the law. 271 F.3d at 1303-04. The juror at issue's "own testimony on her commitment to following the law was not certain." Id. at 1304. While only a majority of jurors stated that the discharged juror was not engaging in deliberations, id. at 1303-04, the juror's own statements revealed her inability to follow the oath she took as a juror.
The instant case is much more similar to Abbell than Brown and Thomas. The District Court carefully and patiently examined the jurors on multiple occasions to isolate the root of the allegations of misconduct. After the District Court received near-unanimous reports that Juror 11 was biased, and after hearing a manifestly incredible rendition from Juror 11, the Court discharged Juror 11. The evidence was so overwhelming that Juror 11 was biased that it would have been "a dereliction of duty for a judge to remain indifferent." Thomas, 116 F.3d at 616. Accordingly, we will affirm the District Court's decision to discharge Juror 11.

IV.
For the foregoing reasons, we will affirm Kemp's, Holck's, Umbrell's, Hawkins's, and Knight's judgments of conviction.
NOTES
[*]  Honorable Eugene E. Siler, Jr., Senior United States Circuit Judge, U.S. Court of Appeals for the Sixth Circuit, sitting by designation.
[1]  The defendants were initially indicted on June 29, 2004. For simplicity, all references to the indictment refer to the superseding indictment.
[2]  White passed away before trial.
[3]  These are but a selection of the charges included in the indictment. Overall, Kemp was charged with one count of conspiracy, 20 counts of wire fraud, 12 counts of mail fraud, three counts of making false statements to a bank, four counts of money laundering, four counts of filing false tax returns, one count of extortion, and one count of attempted extortion; Hawkins was charged with one count of conspiracy, four counts of wire fraud, and four counts of perjury; Knight was charged with one count of conspiracy, three counts of wire fraud, and three counts of making false statements to the FBI; and Holck and Umbrell were charged with one count of conspiracy, eight counts of wire fraud and one count of mail fraud. White was the subject of 38 counts.
[4]  We construe the evidence in the light most favorable to the government, as the verdict winner. See, e.g., United States v. Dobson, 419 F.3d 231, 234 (3d Cir.2005).
[5]  White arranged for Kemp to receive tickets to the NBA All-Star Game and concomitant festivities; two $5,000 checks from Hawkins; a $10,350 deck; transportation and tickets to the Super Bowl in San Diego as well as accommodation and meals; four tickets to a USA basketball game; trips to New York and Detroit; and numerous meals. Moreover, White promised to help Kemp advance his post-treasurer career.
[6]  For instance, in an April 28, 2003 phone call, White and Kemp discussed the composition of several bond teams. Kemp noted that White had been selected as counsel for each deal, so the two focused on underwriters. An excerpt of the telephone call illustrates White's massive authority:

Kemp: And you wanted Loop on there.
White: Ah . . .
Kemp: On the UBS, First American and Loop.
White: Yeah. . . . [A]lso I would like . . . Janney Montgomery Scott.
Kemp: Okay.
White: All right?
Kemp: All right.
White: If I gotta take Siebert off, well, if I, we gotta take somebody off I definitely want Janney Montgomery Scott on there. So we addin' Loop, you say, and Janney Mont . . .
Kemp: You . . . wanted UBS, First American, Loop, and you want Janney.
White: Yeah.
Kemp: Okay, all right.
(App. 11983-84.)
A February 25, 2003 phone call found Kemp and White gloating about their successes: after White instructed Kemp to offer a spot to a particular individual, Kemp stated, "Not a problem at all. Yeah. So, . . . we got the whole rest of the team." White responded, "Right. We're finally doing it the way they use to do us, right? It's terrible, ain't it brother?" Kemp replied, "Oh no, it's life. Oh, it's life man." (App. at 11707.)
Kemp and White's mode of operation is clearly illustrated in their conversation about Andre Allen, a principal of a Philadelphia financial advisory firm, who was seeking business from the city. Right off the bat, White asked Allen for a $25,000 contribution to the mayor's reelection campaign, and Allen promised to consider the request. Soon thereafter, Kemp and White discussed this situation:
White: [Allen] called me, today . . . He called me, you know, because I, I asked him . . . if he could raise twenty-five grand. . . . Called me you know, crying, talkin' about he couldn't do it. . . . Then he started askin' me, well, man, if, you know, if you all deliv-, and I said, listen, man, how many times I got to tell you, don't have that conversation with me.
Kemp: Right.
White: You know what I mean, don't have no quid pro quo conversations with me, I don't have those kinds of conversations. You know, I said listen, I ain't got time to convince you, man, you know. Like, we sat down and we spent a lot of time with you, and we told you, you know, you was going to be part of the team. Now, you know, yous either, you down or you ain't with it.
Kemp: Right, right. . . . `Cause if they don't, if they ain't with it they ain't going to get nothin'.
White: That's right.
Kemp: You know, you, you just hate to say it, but that's the way it is. . . . You know it's not a hard decision. You know, because that stuff comes, comes back, over and over.
(App. 12973-74.)
[7]  For instance, in the February 25, 2003 phone call, Kemp reported that he had been asked to include Pryor, McClendon, a financial firm, and Schnader, Harrison, a law firm, on the Drexel University bond team. White strenuously objected to these firms, and stated, "[Y]ou tell him Pryor McClendon is out, forever." White went on to demand that Schnader, Harrison also be excluded, explaining that "they don't do nothin' for nobody." (App. at 11705.) While Schnader, Harrison earned more than other law firms in fees from bond deals while Kemp's predecessor was treasurer, during Kemp's tenure, they were not selected for a single deal.
[8]  Philadelphia assembled a "bond team" to handle the issuance of bonds. This team included, among other professionals, a lead underwriter, other underwriting banks, separate counsel for the issuer and bondholders, and a printer for the financial documents.
[9]  White, who was on Commerce's payroll as a consultant, aided in these efforts.
[10]  The jury found Kemp not guilty of eight counts of wire fraud, one count of making false statements to a bank, and four counts of money laundering; Hawkins not guilty of conspiracy, three counts of wire fraud, and one count of perjury; Holck and Umbrell not guilty of three counts of wire fraud; and Knight not guilty of one count of wire fraud. The jury was unable to reach a verdict as to Kemp on four counts of wire fraud and one count of mail fraud; as to Holck and Umbrell on two counts of wire fraud and one count of mail fraud; and as to Knight on the conspiracy charge, two counts of wire fraud, and one count of making false statements to the FBI. The government withdrew one count of wire fraud against Kemp, Holck, and Umbrell.
[11]  Kemp does not dispute that as treasurer, he was a public official who owed a duty to provide honest services to the public. See 65 Pa. Cons.Stat. § 1102; see also Antico, 275 F.3d at 262 n. 18.
[12]  This case is distinguishable from United States v. McNeive, 536 F.2d 1245 (8th Cir. 1976), where the Eighth Circuit concluded that a chief plumbing inspector's acceptance of unsolicited gratuities that were attached to applications for permits that required only ministerial action did not amount to honest services fraud. Id. at 1251. Even if Kemp's actions here were largely ministerial, Kemp's role in setting the scheme in motion and then demanding payment was of a far more insidious order than the passive behavior of the defendant in McNeive.
[13]  These instructions were consistent with Pennsylvania law, which requires public officials to report "[t]he name and address of the source and the amount of any gift or gifts valued in the aggregate at $250 or more and the circumstances of each gift," 65 Pa. Cons. Stat. § 1105(b)(6); in defining "gift," the statute excludes from the general definition "a commercially reasonable loan made in the ordinary course of business," §§ 1102, 13A03.
[14]  The District Court instructed the jury that to determine whether the loans provided to Kemp were gifts that were required to be reported, it should consider "whether defendant Holck and/or defendant Umbrell followed established Commerce Bank procedures applicable for similar loans, whether they intended to give a benefit or gift to defendant Kemp, whether the loans were commercially reasonable, made in the ordinary course of business, whether the loans were considered by defendant Kemp to be a benefit or gift, the terms of the loan and other factors . . . that you consider material." (App. at 9651.) This appropriately conveyed to the jury the many-faceted issue.
[15]  While we made that statement while discussing the Hobbs Act, it is no less applicable in the present context. See, e.g., United States v. Woodward, 149 F.3d 46, 57 (1st Cir.1998) (permitting similar form of proof in honest services fraud case).
[16]  Indeed, given that the government must also prove the loan was given in exchange for some official action, there is little danger that honest loans will trigger criminal liability.
[17]  Because we have rejected Holck and Umbrell's arguments that the failure to disclose theory was legally invalid, see part III.B.3., supra, we need not consider whether the District Court correctly concluded that the government presented insufficient evidence to convict on the failure-to-disclose theory. As we discussed above, because the evidence was "sufficient to convict on another alternative theory that was charged to the jury in the same count, [we will] assume that the jury convicted on the factually sufficient theory and [will] let the jury verdict stand." Syme, 276 F.3d at 144.
[18]  Our jurisprudence distinguishes between challenges to the sufficiency of the evidence, in which the appellant claims that the government failed to prove an essential element of conspiracy, and variance claims, in which the appellant argues that the government proved multiple conspiracies instead of the one charged in the indictment. For instance, in United States v. Kenny, 462 F.2d 1205 (3d Cir.1972), we explained, before commencing our variance analysis, that it was "not a case where there was no evidence of the existence of a conspiracy"; rather, the government allegedly "proved several separate unrelated conspiracies under each conspiracy count." Id. at 1216. Similarly, in United States v. Perez, 280 F.3d 318 (3d Cir.2002), we considered both sufficiency of the evidence and variance challenges to the same conspiracy conviction. Id. at 342. The sufficiency of the evidence analysis concerned whether the defendants possessed the "requisite knowledge of the illegal objective of the scheme to distribute methamphetamine such that they could form an intent or agreement to join the conspiracy." Id. at 343. One defendant claimed that he was caught with a drug distributor only by chance and was not involved with drugs, while the other claimed that he had a common buyer-seller relationship with the distributor and was not involved in a conspiracy to distribute. Id. This can be contrasted to the variance argument, where the defendants argued that while they may have been involved in a conspiracy to distribute drugs in New York, they were not part of the same conspiracy as men who dealt drugs in New Jersey. Id. at 347. Because Holck and Umbrell concede that the government presented sufficient evidence that they were involved in a conspiracy with some, but not all, of their co-defendants, we interpret their claim as alleging a prejudicial variance, rather than as a pure sufficiency of the evidence challenge.
[19]  In the typical chain conspiracy, the actions of each co-conspirator benefit the overall conspiracy. It is for this reason that the "chain conspiracy" cases relied on by the Government are of limited relevance to our discussion. The paradigmatic example in which the chain metaphor provides guidance is the drug conspiracy, where the conspirators often "share a common goal, such as the possession and distribution of narcotics for profit." See United States v. Tarantino, 846 F.2d 1384, 1393 (D.C.Cir.1988); United States v. Russell, 134 F.3d 171, 182 (3d Cir.1998) (stating that "the common goal of this conspiracy was to make money selling cocaine"); United States v. Quintero, 38 F.3d 1317, 1337 (3d Cir.1994) ("The prosecution must . . . demonstrate that a defendant, charging variance, knew that he was part of a larger drug operation."); United States v. Barr, 963 F.2d 641, 650 (3d Cir. 1992); Salmon, 944 F.2d at 1117 (conspiracy to sell cocaine for profit or another benefit); Padilla, 982 F.2d at 115 (stating that "there was a common goal to obtain and sell cocaine for profit and knowledge attributable to [the defendant] of a larger network"); United States v. Kelly, 892 F.2d 255 (3d Cir.1989) (conspiracy to possess and manufacture methamphetamine); id. at 258 (describing the Government's theory as the "classic chain conspiracy"). We do not wish to imply that every individual involved with a drug conspiracy is necessarily a member of that one conspiracy. "[E]ven if we determine that a chain conspiracy exists, we may still conclude that certain actions were outside the chain and formed a separate conspiracy." Tarantino, 846 F.2d at 1393.
[20]  Specifically, Bradley Himmeger, the Blockbuster representative, testified that despite Hawkins's testimony that he owned 55 Blockbuster Video stores, Hawkins actually owned zero. H. Van Sinclair, a representative of BET, testified that contrary to Hawkins's claim that he was a partner of Bob Johnson in the sale of BET for $3.5 billion, the two men were not partners and Hawkins was not involved in the sale. Pizza Hut representative John Murphy contradicted Hawkins's claim that he had sold 127 restaurants back to Pizza Hut by testifying that Hawkins had returned 72 restaurants to Pizza Hut and had actually paid Pizza Hut $50,000 to take the debt-ridden restaurants off his hands. Finally, W. Barry Blum, a representative of Burger King, testified that Hawkins received only $95,000 when he sold restaurants to Burger King, not, as Hawkins had claimed, $35 million.
[21]  Similarly, after a grand juror asked Hawkins whether, during the meeting with Khan, White, and Kemp, he discussed using the Philadelphia pension funds to finance one of his endeavors, Hawkins immediately harkened to his wealth. He answered:

No. As a matter of fact to be perfectly honest with you my partner is Bob Johnson. We own BET for 3.5 billion dollars. So back in 2002 we sold it as a matter of fact to Viacom. So you know Bob Johnson is a partner of mines, Ted Turner has been a partner of mines. So we've got Leonard Greenwood. We got five different companies that because I've been so success[ful] in the fast food business that I have partners that raise eight, nine billion dollars in private placement that's what we're going to do. We were putting, 250 million dollars was going to be used in equity and the rest of the money was going to be raised by Merrill Lynch. They're going to handle the debt.
(App. at 14822-23.)
[22]  The District Court also limited the extent that financial information could be admitted by requiring that the evidence be presented succinctly and without confusing the jury.
[23]  We recognize that several courts of appeals have concluded that evidence of consciousness of guilt is intrinsic to the charged offense, and thus outside Rule 404. For instance, in United States v. Simmons, 470 F.3d 1115, 1124-25 (5th Cir.2006), the Fifth Circuit permitted the government to introduce a defendant's prior testimony that he had given in a state trial concerning an alleged sexual assault for the purpose of proving, through other evidence, that those statements were false. Id. at 1125. The court explained:

Similarly, Simmons' state-court testimony was not inadmissible under Rule 404(b) because it did not constitute a separate extrinsic bad act. The prior testimony was relevant to issues other than Simmons' bad character. It was introduced not to show Simmons lied in the past, was a bad person, and, therefore, must have sexually assaulted Robinson; rather, it was introduced to show his consciousness of guilt and that he had lied in order to fabricate an alibi.
Id.; see also United States v. Frost, 234 F.3d 1023, 1025 (8th Cir.2000) ("Frost's testimony is direct evidence of fraudulent intent and consciousness of guilt. It does not relate to `other acts,' but rather constitutes evidence intrinsic to the overall scheme. Rule 404 is therefore inapplicable."); United States v. Ramirez-Jiminez, 967 F.2d 1321, 1327 (9th Cir. 1992) (explaining evidence that defendant had lied to government agents when stopped during crime was "probative of his consciousness that his conduct was illegal" and therefore Rule 404(b) was inapplicable).
However, we have previously approved the admission of evidence of consciousness of guilt under Rule 404. See Gatto, 995 F.2d at 455 (explaining that testimony was "admissible under Rule 404(b) . . . to show consciousness of guilt"). We thus follow our precedent and examine this issue under Rule 404. Given that we have concluded that consciousness of guilt is a proper purpose under Rule 404, however, our analysis converges with that used by the cases that hold Rule 404 inapplicable.
[24]  We expressly left this issue open in Boone. See 458 F.3d at 329 n. 4.
[25]  We note that in many instances of bias, a district court will be able to focus on the existence of a particular act that gives rise to the bias. See, e.g., United States v. Egbuniwe, 969 F.2d 757, 763 (9th Cir.1992) (source of anti-prosecution bias stemmed from a particular incident of an alleged "false arrest and rough treatment of [a juror's] girlfriend by law enforcement officers"). The rule we announce today does not apply to the type of bias that does not require the District Court to investigate a topic that implicates the secrecy of jury deliberations. See Symington, 195 F.3d at 1087 n. 6; Thomas, 116 F.3d at 621.
[26]  The need for such a high standard prior to dismissal comes from a federal criminal defendant's Sixth Amendment right to a unanimous jury verdict. If the Government is able to remove a holdout juror because of ambiguous allegations of improper behavior during deliberations, and replace this holdout with a more amenable juror, then the defendant's constitutional right to a unanimous verdict has been violated. Put differently, each juror must find the defendant guilty beyond a reasonable doubt. We are convinced that the "beyond a reasonable doubt" standard best protects a defendant's constitutional right to a unanimous verdict. A hypothetical illustrates our concerns. Assume that Juror X is a holdout. Assume that Juror X wants to vote to acquit the defendant. If a district court finds, by a mere preponderance of the evidence, that Juror X's act of holding out is causally due to bias, then there is an up to 49% chance that Juror X's belief in acquittal is causally traced to Juror X's belief in the defendant's innocence. But if Juror X is removed from the jury, then the defendant loses out on having a holdout juror who legitimately (i.e., on the merits) believes that the government has not satisfied its "guilty beyond a reasonable doubt" standard. The only way to satisfy the defendant's constitutional right to a unanimous verdict in the juror discharge context is to only permit removal when the District Court finds, beyond a reasonable doubt, that the holdout's reasons were not related to the merits of the case.
[27]  We also note that, in this case at least, the final interview with the jurors controls the inquiry. Even though  among other complaints  the jurors claimed that Juror 11 was biased before the first voir dire and immediately after the second, the District Court never questioned the jury about this until the third voir dire. Thus, the third voir dire was the first chance for each juror to fully detail any concerns that he or she had about Juror 11's bias. Further, it was before the final voir dire that the District Court comprehensively distinguished between permissible and impermissible bias.
