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JULIE CARNES, Circuit Judge: The defendants in this case — George Ca-vado, his wife Paula Hornberger, and Joel Streinz — were players in one of the most long-lasting mortgage fraud conspiracies in the history of central Florida. From approximately October 1997 through March 2008, these three defendants, along with about a dozen other people, conspired to solicit and assist friends, family members, and business associates to fraudulently purchase and sell over thirty residential real estate properties that were ultimately used as primary residences or for investment purposes. Fifteen of the defendants’ cohorts pled guilty either to the conspiracy count or to at least one substantive count. Only Ca-vado, Hornberger, and Streinz went to trial, and, after a three-month trial, the jury convicted each of them on the count charging conspiracy to commit wire fraud and to make false statements to an FDIC-insured bank in violation of 18 U.S.C. § 371. Ca-vado and Hornberger were also convicted of one substantive count of making false statements to an FDIC-insúred bank in violation of 18 U.S.C. § 1014. Cavado was sentenced to 120-months imprisonment. Hornberger was sentenced to twelve months and one day imprisonment. Both were ordered to pay over $13 million in restitution. Streinz was sentenced to 60-months imprisonment and ordered to pay $2,322,676 in restitution. A11 three appeal their convictions. Cavado and Hornberger also appeal their sentences. After careful consideration of the record and all the briefs, we affirm Caval-lo’s and Hornberger’s convictions and sentences, except that we vacate and remand the orders of restitution issued as to them. We reverse and vacate Streinz’s conviction. I. BACKGROUND The leader of the conspiracy, Craig Adams, devised and led the fraud scheme, which was referred to at trial as “Craigo-nomics.” The conspirators would fraudulently obtain the maximum amount of possible loans for each property by using false statements on mortgage applications, allowing the conspirators to minimize the funds needed for closing. .The parties would then sell, or “flip,” the properties to turn a profit. To accomplish this objective, the conspirators would falsely inflate the sale price of properties in the loan documents they submitted to lenders and then resell the properties either among themselves, as “friendly” buyers and sellers, or to others outside the conspiracy. To further reduce the amount of money needed for closing, the conspirators sometimes obtained second mortgages from different lenders without disclosing the first mortgage. The loan applications contained material falsehoods concerning: (1) the purchaser’s and/or buyer’s income, assets, and liabilities; (2) the purchase or sale price; (3) the amount and source of the down-payment; (4) the identity of the seller and purchaser/borrower; (5) the familial relationship of the parties; (6) the purchaser’s/borrower’s intended use of the property; and (7) the disbursement of the loan proceeds. Some conspirators lived in the fraudulently-acquired homes, but because most could not afford the mortgage payments and maintenance costs of the properties, they rented out the homes for additional income. Even then, the borrowers experienced cash flow problems, and they often took out home equity loans on their existing properties or acquired new properties and fraudulently extracted cash from them. The leader of the scheme, Craig Adams, initiated, and orchestrated the conspiracy by locating properties and recruiting individuals to participate. Adams, who pled guilty, recruited Richard Bobka, who is defendant Cavallo’s brother, to act as a real estate agent, buyer, and seller. Bob-ka then partnered with Cavallo and Caval-lo’s wife, defendant Hornberger, to fraudulently obtain more properties. On several occasions, Hornberger served as a friendly buyer because she had a good credit score. Cavallo handled the bookkeeping, banking, and taxes for many properties that he and Hornberger acquired with Bobka. Cavallo and Hornberger listed several of the fraudulently-acquired properties on their joint tax returns by claiming rental income and expenses. Cavallo, Bobka, and Horn-berger maintained a joint bank account that they used to hold the fraudulently-acquired loans. Bobka also recruited defendant Joel Streinz to participate in the conspiracy as a friendly buyer and seller for two properties. On appeal, the three defendants before us raise several issues. Streinz argues that the district court violated his Sixth Amendment right to counsel when the court prohibited him from consulting with his attorney during the time period in which he was testifying: a period that covered three days of trial and two overnight recesses. Cavallo argues (1) that there was insufficient evidence to convict him of making false statements to an FDIC-insured bank in violation of 18 U.S.C. § 1014 and (2) that his sentence is substantively and proeedurally unreasonable. Cavallo and Hornberger, together, argue that the district court erred in (1) ordering and calculating restitution and (2) using sidebar conferences in violation of their Sixth Amendment right to a public trial. Finally, all three defendants argue that the district court erred by: (1) failing to fully investigate possible juror misconduct; (2) failing to conduct an evidentiary hearing on allegations of witness misconduct in grand jury; and (3) failing to conduct an evidentiary hearing on alleged defense witness intimidation. We address first any contentions that challenge the validity of a conviction, after which we turn to challenges to the sentences imposed. II. STREINZ’S ACCESS TO COUNSEL CLAIM A. Background After his co-defendants had rested their cases, Streinz informed the court that he wanted to testify on his own behalf. That testimony was delayed, however, because on the morning that Streinz’s testimony was scheduled to begin, Government counsel-informed the trial court that Streinz had just produced documents that were pertinent to his testimony and that should have been provided much earlier, during discovery. The district court convened, a hearing, and Streinz testified that he had recently found the documents at home, while preparing for trial. At the Government’s request, the court ordered Streinz, his attorney, the prosecutor, and a federal agent to go to Streinz’s house to retrieve any other documents that were subject to discovery. The court recessed the proceedings, postponing Streinz’s testimony and directing him “not to communicate with anyone whatsoever with regard to the documents located at your home.” Accompanied by the prosecutor, a detective, a federal agent, and his own attorney, Streinz traveled to his home. Upon entering the house, the group went directly to an office that contained stacks of papers that Streinz had been examining in preparation for trial. The situation became heated, with Streinz asserting that the officers were engaging in a more intrusive search than was appropriate for their limited mission, and with the detective, who contended that Streinz was pot complying with the officer’s directives, ultimately calling for backup. To prevent matters from getting further out of hand, Streinz’s attorney quickly tried to identify any pertinent documents and brought those documents to the courtroom, where the prosecutor began reviewing them. While examining these papers, the prosecutor saw a handwritten notation indicating that the documents contained Streinz’s work product. Concerned that he might be improperly examining a defendant’s work product, the prosecutor ceased his review and asked Streinz’s attorney to keep the documents in a box in the courtroom in case an issue arose. Streinz’s attorney moved for a mistrial the next morning, arguing that his defense had been compromised by the document retrieval and review procedure. The court denied the motion and asked Streinz if he still wanted to testify. Streinz indicated that he did, although he expressed concern that his defense had been “jeopardized” by the previous day’s events. Streinz’s direct examination then began. As the trial recessed at the end of the day, the court instructed Streinz that he' could not discuss his testimony with “anyone,” but that he could talk to his lawyer about his “constitutional rights.” The court did not, however, explain what that phrase might mean. Prior to resuming his direct testimony the next day, Streinz sent a letter directly to the court expressing distress at his situation. As set out in that document, Streinz noted uncertainty whether it was appropriate to send the judge a letter, but, given the court’s earlier restriction on conversations with his attorney, he felt that he could not talk with the latter about his concerns without “cross[ing] a line of violating the court[’s] restrictions.” Streinz stated, among other things, that his preparation, particularly for cross-examination, had been hampered because he had been deprived of trial documents that were “seized without any advance notice,” thereby preventing him from being able to inventory or make copies of the documents. The court acknowledged Streinz’s letter and, while the other trial participants remained waiting in the courtroom, allowed Streinz, on his own and without any consultation with his attorney, to review the documents taken from his home. After he had finished reviewing the documents in the courtroom, Streinz completed his direct examination, and cross-examination began. Streinz was still on the stand being cross-examined when the trial day ended. The district court again reminded him that, although he could talk to his lawyer about “constitutional rights” during the overnight recess, he could not talk to his lawyer “about the case.” Again, the court did not explain what a discussion about Streinz’s constitutional rights might entail. The next morning, Streinz sent a second letter to the court. In this letter, Streinz expressed his anxiety that, because the court would not allow him talk to his lawyer, no one was “looking out” for his “interests and due process.” He also advised the court that the time he had been given to review his documents in court on the previous day was insufficient, considering that he had been deprived of the documents for three days. In particular, he noted, the Government had referenced one of those documents in court the day before and likely would do so again, and Streinz had no access to that document to better prepare himself for cross-examination. He concluded by suggesting that errors made by the Government, his attorney, and the court were “sabotaging [his] ability to be prepared and properly defend [his] case.” The district court acknowledged Streinz’s complaint but indicated that the documents had been available to Streinz ever since his attorney, in the company of Government personnel, had retrieved them from Streinz’s home. (But as Streinz was not supposed to be talking to his attorney about the case, it is unclear how Streinz would have known that he could have requested his lawyer to hand over the documents to him.) Regarding the impact of any errors on Streinz’s right to testify, the court reminded Streinz that it had previously informed him that he had a constitutional right not to testify. Then, after giving Streinz forty additional minutes to review the documents in the courtroom, cross-examination began again. B. Discussion Streinz argues that his Sixth Amendment rights were violated by the trial court’s refusal to allow him to confer with counsel during the two overnight recesses while he was testifying. We agree. We review Streinz’s Sixth Amendment claim pursuant to a de novo standard. See United States v. Williams, 527 F.3d 1235, 1239 (11th Cir.2008) (reiterating that claims of constitutional error are reviewed de novo). A trial is deemed unfair if the accused is denied counsel at a critical stage of his trial. See United States v. Cronic, 466 U.S. 648, 659, 104 S.Ct. 2039, 80 L.Ed.2d 657 (1984). The question here is whether, by prohibiting Streinz from speaking to his attorney about his case during the three days he was on the witness stand — including the two overnight recesses — the district court deprived Streinz of assistance of counsel at a critical stage of the proceedings. We conclude that the district court’s restriction did so deprive Streinz. This conclusion is dictated, for the most part, by the Supreme Court’s decision in Geders v. United States, 425 U.S. 80, 91, 96 S.Ct. 1330, 47 L.Ed.2d 592 (1976). In Geders, which was also tried in the Middle District of Florida, the district court had directed defendant Geders not to talk to his attorney “about anything” during a seventeen-hour overnight recess between his direct and cross-examination. Id. at 83 n. 1, 96 S.Ct. 1330. Geders’ attorney objected, explaining that he had a right to talk to his client about matters other than the imminent cross-examination. The district court declined counsel’s request, noting that the latter could talk to Geders, while remaining in the courtroom, about the witnesses to be called the next day, but nothing more than that. Further, the court assured counsel that he would be able to consult with Geders once the latter’s cross-examination had concluded and before redirect examination, and the court did allow that post-cross-examination consultation the next day. Id. at 82-85, 96 S.Ct. 1330. In determining whether the district court’s sequestration of Geders from his own attorney during the overnight recess violated Geders’ constitutional right to counsel, the Supreme Court acknowledged that, as a general rule, valid reasons exist for disallowing a witness who is testifying from speaking to trial counsel at recess periods during that testimony. The main justification for this prohibition is the interest in deflecting efforts by third-parties to coach the witness before he returns to the stand the next day to face cross-examination. Id. at 87, 96 S.Ct. 1330. Yet, as the Court noted, a criminal defendant is not just another witness. Although a non-party witness will likely have little to discuss with trial counsel other than his upcoming testimony, an accused and his attorney will often have many other matters to discuss during an overnight recess. Indeed, the Court noted, “[s]uch recesses are often times of intensive work, with tactical decisions to be made and strategies to be reviewed.” Id. at 88, 96 S.Ct. 1330. For example, defense counsel “may need to obtain from his client information made relevant by the day’s testimony, or he may need to pursue inquiry along lines not fully explored earlier. At the very least, the overnight recess during trial gives the defendant a chance to discuss with counsel the significance of the day’s events.” Id. Although it was sympathetic to a district court’s desire to minimize the opportunities for a witness to be coached during a long recess, the Supreme Court nonetheless determined that an accused’s right to confer with counsel trumps a court’s concerns about such consultation. Specifically, when there is a conflict between a testifying defendant’s right to consult with his attorney during “a long overnight recess” and the prosecutor’s desire to eliminate the risk that defense counsel will coach his client before the latter’s cross-examination, “the conflict must, under the Sixth Amendment, be resolved in favor of the right to the assistance and guidance of counsel.” Id. at 91, 96 S.Ct. 1330. Geders’ conviction was overturned because the trial court would not let him talk to his lawyer during one overnight recess. The district court here, in effect, restricted Streinz from talking to his attorney during two overnight recesses that occurred while he was testifying. Thus, on its face, Ged-ers appears to call for reversal of Streinz’s conviction. The Government, however, disagrees that Geders requires a conclusion that Streinz’s right to counsel was violated, and we now turn to those distinctions that the Government says exist between this case and Geders. First, the Government cites language, here and there, from Perry v. Leeke, 488 U.S. 272, 109 S.Ct. 594, 102 L.Ed.2d 624 (1989), in support of its argument that Streinz’s right to counsel was not compromised by the district court’s broad embargo on conversations between Streinz and his attorney. But it is difficult to discern how Perry bolsters the Government’s position. In Perry, the trial Court had only prohibited the defendant from consulting with his attorney during a fifteen-minute recess that occurred after the defendant’s direct testimony had concluded and before cross-examination was to begin. Id. at 280, 109 S.Ct. 594. Given the timing and short duration of the recess, the Supreme Court distinguished Geders and concluded that the defendant’s right to assistance of counsel had not been compromised by sequestration from his attorney during such a brief period of time. In reaching this conclusion, the Court noted that a defendant has no constitutional right to consult with his lawyer while testifying. Id. at 281, 109 S.Ct. 594. In other words, if a defendant gets in a tight spot; on cross-examination, “neither he nor his lawyer has a right to have the testimony interrupted in order to give him the benefit of counsel’s advice.” Id. Were a defendant allowed to huddle with his lawyer whenever the going gets tough, the truth-seeking function of the trial would be impeded. And if a defendant has no right to call a time-out to talk with counsel during his testimony, he similarly has no right to take advantage of a fortuitously-timed recess “in which there is a virtual certainty that any conversation between the witness and the lawyer would rélate to the ongoing testimony.” Id. at 283-84, 109 S.Ct. 594. But, in terms of the right to assistance of counsel, a period of silence between a criminal defendant and his attorney during a short recess was a far different matter for the Perry court than would be a similar quarantine during an overnight recess. Reaffirming Geders, the Court noted that during an overnight recess, normal consultation between defendant and counsel would “encompass matters that go beyond the content of the defendant’s own testimony,” including the availability of other witnesses, trial tactics, or even negotiating a plea agreement. Id. at 284, 109 S.Ct. 594. And the “fact that such discussions will inevitably include some consideration of the defendant’s ongoing testimony does not compromise that basic right.” Id. In short, we read Perry as reaffirming the validity of the Geders principle. The district court’s restriction on Streinz’s ability to consult with his attorney during two overnight recesses clearly “falls on the Geders side of the line and violates the Sixth Amendment.” United States v. Sandoval-Mendoza, 472 F.3d 645, 651 (9th Cir.2006) (holding that Geders precludes “any overnight ban on communication”); see also Perry, 488 U.S. at 284, 109 S.Ct. 594 (“It is the defendant’s right to unrestricted access to his lawyer for advice on a variety of trial-related matters that is controlling in the context of a long recess.”). In fact, this case involves the kind of communications that Geders intended to protect. The day before Streinz began his direct examination, the Government ■ had taken documents and work product from Streinz’s house that he needed to prepare for his testimony. Thereafter, and throughout his direct and cross-examination, Streinz’s access to the documents was limited to brief, in-court review sessions. As both Streinz and his attorney interpreted the court’s instruction, Streinz could not confer with his attorney even to determine whether or how he could regain possession of the documents. Nor could he discuss with his attorney the likelihood that his defense had been compromised by the Government’s retrieval and review process, or any means to reduce that threat. See Geders, 425 U.S. at 88, 96 S.Ct. 1330 (“At the very least, the overnight recess during trial gives the defendant a chance to discuss with counsel the significance of the day’s events.... [T]he role of counsel is important precisely because ordinarily a defendant is ill-equipped to understand and deal with the trial process without a lawyer’s guidance.”). The Government argues that the district court did not actually prevent Streinz from conferring with counsel during overnight recesses, or even during in-court recesses, because the court told Streinz' several times that he could discuss with his lawyer his “constitutional rights.” We do not know what the district court meant by this exemption, and it appears obvious that neither did Streinz. Clearly, Streinz was of the impression that the court had forbidden him from consulting at all with his attorney about his case, which was not an unreasonable assumption because those were the court’s exact words. Otherwise, he would not have felt compelled, during the course of his testimony, to write the court two letters revealing his concerns, and particularly his need for access to documents that the Government had taken from his home on the day his direct examination was to have begun. Indeed, Streinz told the judge, outright, that he had written the letter rather than dealing through counsel because he did not want to run afoul of the court’s order against communications between him and his attorney. As to what one could reasonably assume the district court to have meant by the phrase “constitutional rights,” when the court told Streinz not to speak to his attorney about anything except those rights, the court had previously and consistently used this term to refer to Streinz’s Fifth Amendment right against self-incrimination. But any discussion about Streinz’s right against self-incrimination would have been a very short conversation because Streinz had already begun testifying, and any right he might have earlier had not to incriminate himself had, by that time, become a moot point. And even if we assume that the district court intended to permit communication on a broader array of subjects than just Streinz’s right against self-incrimination, its instruction that Streinz should not talk to his attorney about “the case” during an overnight recess did not comply with Geders. See Perry, 488 U.S. at 284, 109 S.Ct. 594 (noting the wide variety of trial-related communications that are protected by Ged-ers and stating that the “fact that such discussions will inevitably include some consideration of the defendant’s ongoing testimony does not compromise” a defendant’s right to assistance of counsel during an overnight recess). Finally, citing Crutchfield v. Wainwright, 803 F.2d 1103 (11th Cir.1986) (en banc), the Government makes a two-fold argument (1) that Streinz failed to preserve this issue on appeal because he did not object to the district court’s restriction and (2) that there is no indication that Streinz actually wanted to talk to his attorney during the overnight recesses. In Crutchfield, the state trial court called a brief recess during defendant Crutchfield’s direct testimony and instructed defense counsel not to discuss the defendant’s testimony with him during that break. Crutchfield did not object. Id. at 1104. After conviction, and relying on Geders, Crutchfield filed a federal habeas corpus petition, arguing that the trial court’s restriction on his communication with his attorney deprived him of the assistance of counsel. The en banc court unanimously agreed that the conviction should not be vacated, but three opinions were issued, with each opinion reflecting different reasoning in support of this outcome. A six-judge plurality of the en banc court concluded that Geders applied even to short recesses within a trial day and assumed that the trial court’s admonition to Crutchfield did unconstitutionally restrict his right to the assistance of counsel during that recess. Id. at 1104-1111. But in Geders, the defendant had objected to the proscription against consultation. Crutchfield neither objected to the court’s instruction nor did the record reflect that there was a desire to consult by either him or his counsel. Accordingly, because a defendant must show that the prohibition against consultation actually prevented him from conferring with counsel, the plurality concluded that Crutchfield had failed to show a deprivation of his right to assistance of counsel. Id. at 1109-11. The five-judge concurring opinion read the plurality opinion as establishing a per se rule that any restriction by the trial court on the ability to confer with counsel during any recess, no matter how short in duration, constitutes a deprivation of counsel. Id. at 1116. Viewing that analysis as too simplistic, the concurring opinion indicated that when dealing with a non-overnight recess, one should look at several factors. And given the relatively short recess and the limited admonition by the trial court, the concurring opinion concluded that Crutchfield had not suffered a constitutional deprivation of the right to counsel. Id. at 1115-16. Further, the concurring opinion not only disagreed with the plurality opinion’s application of a per se rule to the question whether an error had occurred, but also found fault with the latter’s application of a per se rule requiring a contemporaneous objection to preserve that error for review. Id. at 1118. The concurring opinion noted that the plurality’s rule would mean that a trial court could prevent a defendant from speaking to counsel during a week-long recess— which under Geders would clearly constitute a constitutional error — but if no objection were made, the error would not be deemed preserved: a result that the concurring opinion concluded would not be consistent, in all cases, with established principles concerning the waiver of constitutional rights. Id. As noted, two years after this Court’s decision in Crutchfield, the Supreme Court issued its decision in Perry, concluding that a trial court’s restriction of consultation between a testifying defendant and his counsel during a brief recess does not constitute a deprivation of the defendant’s right to counsel. Thus, that part of the Crutchfield plurality decision holding invalid even a brief restriction of consultation between a defendant and his attorney is no longer good law. As to the plurality’s requirement that a contemporaneous objection be lodged to preserve error when such restrictions on consultations are imposed by a trial court, we need not decide whether such an objection would be required in all circumstances because we conclude that Streinz did object to the district court’s imposition of a restriction on his right to consult with counsel and that the prohibition against consultation actually prevented Streinz from conferring with his attorney. Here, although Streinz’s two letters to the district court did not contain the phrase, “I object,” he clearly conveyed the distress and confusion that the court’s restrictions were causing him. See United States v. Johnson, 267 F.3d 376, 380 (5th Cir.2001) (holding that, after the district court prohibited counsel from consulting with the defendant during two overnight recesses occurring while the defendant was testifying, counsel “made .clear his desire to confer with [the defendant],” and was not required to “preface his remarks with the magic words, ‘I object.’ ”); United States v. Isom, 88 F.3d 920, 923 n. 7 (11th Cir.1996) (explaining that although appellants did not use the words “double jeopardy” in their objection below, the substance of their argument was sufficient to preserve a claim under the Double Jeopardy Clause); see also United States v. Munoz, 430 F.3d 1357, 1374 (11th Cir.2005) (agreeing that a defendant may preserve a constitutional objection “in a number of ways, and need not object explicitly on constitutional or Sixth Amendment grounds”). Streinz’s two letters and his colloquies with the trial court adequately conveyed his request to confer with counsel and his belief that his rights were being violated as a result of the court’s refusal to allow him to do so. He therefore alerted the court to the problem and gave it an opportunity to correct any error. See United States v. Turner, 474 F.3d 1265, 1276 (11th Cir.2007) (noting that one of the “fundamental purposes” of the contemporaneous objection rule is to give the trial court an opportunity to address and avoid errors). The district court failed to do so and we therefore conclude that the trial court’s orders prohibiting him from conferring with counsel during two overnight recesses imper-missibly infringed on Streinz’s fundamental right to counsel. Geders, 425 U.S. at 91, 96 S.Ct. 1330; see also Perry, 488 U.S. at 284, 109 S.Ct. 594 (reaffirming that Geders controls in the context of a long recess). For this reason, we REVERSE Streinz’s conviction and remand for a new trial. III. ALLEGED GRAND JURY MISCONDUCT A. Background Defendants Cavallo and Hornberger (“Defendants”) contend that, while testifying before the grand jury that indicted them, a federal agent perjured himself when responding to a grand juror’s question. They appeal the district court’s denial of their motions to dismiss the indictment based on this alleged misconduct. The pertinent facts are as follows. During the course of a day-long grand jury session focusing on the present case, an FBI agent testified about the many documents related to the mortgage fraud conspiracy. After he had discussed at length a specific overt act related to a property on 1762 Southpointe Drive, which overt act was also charged as a substantive offense in Count 37, a grand juror asked the agent a question: GRAND JUROR: On all these — on all these documents that have been signed by these people who are named in the indictment, in each count of the indictment, has it been verified that Bobka, Cavallo, and Hornberger in Count 37 actually signed the documents that they are alleged to have signed? I mean, their name’s been verified that, yeah, that’s truly that person’s signature and they weren’t forged by somebody else? WITNESS: Right. Through the investigation, yes sir, we’ve done that, either through interviews of people, and again, I’ll go back, you know, sometimes— many times admissions that they, going right through it, yes, that’s my signature. Yes, that’s my signature. And many times throughout — the total information that we have from witnesses about who the parties were involved, who was at the closing, what was observed and seen in terms of signing. GRAND JUROR: Okay. WITNESS: So we’ve done it through that way. We — that would be the way that we’ve done it. In their motions to dismiss, Defendants argued that, through this response, the agent essentially testified that every signature on every relevant document in this case had been verified as belonging to the purported signer. This, they argue, was not accurate and thus the agent made a perjurious statement. In support of this assertion, they cite Hornberger’s testimony at trial that a number of signatures on loan documents bearing her name and Ca-vallo’s name were forged by Richard Bob-ka, who had recruited Hornberger and Cavallo to participate in the scheme and who was substantially involved in the purchase, sale, and management of properties with Hornberger and Cavallo. Additionally, Streinz testified that he did not sign several documents bearing his name related to properties on Commonwealth Drive and Anchorage Drive. B. Discussion We review a district court’s denial of a motion to dismiss an indictment for abuse, of discretion but, in determining whether the court abused its discretion, we resolve issues of law de novo. United States v. Schwartz, 541 F.3d 1331, 1355 n. 69 (11th Cir.2008). Likewise, we review a claim of prosecutorial misconduct de novo because it is a mixed question of law and fact. United States v. Duran, 596 F.3d 1283, 1299 (11th Cir.2010). As a general matter, to establish prosecutorial misconduct for the use of false testimony, a defendant must show that the prosecutor knowingly used perjured testimony or failed to correct what he subsequently learned was false testimony, and that the falsehood was material. United States v. McNair, 605 F.3d 1152, 1208 (11th Cir.2010). When the alleged prosecutorial misconduct occurs in the context of a grand jury proceeding, we dismiss the indictment only when the misconduct “substantially influenced the grand jury’s decision to indict” or when there is “grave doubt that the decision to indict was free from the substantial influence of such violations.” Bank of Nova Scotia v. United States, 487 U.S. 250, 256, 108 S.Ct. 2369, 101 L.Ed.2d 228 (1988) (internal quotations omitted). Accord United States v. Verbitskaya, 406 F.3d 1324, 1336 and n. 13 (11th Cir.2005); United States v. Vallejo, 297 F.3d 1154, 1166 (11th Cir.2002). As to the elements of perjury, “perjury” is testimony “given with the willful intent to provide false testimony and not as a result of a mistake, confusion, or faulty memory.” United States v. Ellisor, 522 F.3d 1255, 1277 n. 34 (11th Cir.2008). Yet, an agent’s inadvertent giving of false testimony before the grand jury does not warrant dismissal of an indictment. United States v. DiBernardo, 775 F.2d 1470, 1475 (11th Cir.1985). With the above standards in mind and upon examination of the testimony at issue, we conclude that Defendants have failed to show that the agent’s answer to the grand juror’s question was untruthful. Even if one could assume some inaccuracy in the agent’s response to the grand juror’s imprecisely-worded question, Defendants have failed to demonstrate that the agent intentionally made a false statement, or that the prosecutor would so interpret his testimony. It is Defendants’ thesis that, in response to a spontaneous question by the grand juror, the agent falsely told the grand jurors that investigators had verified that each signature on every pertinent document in the entire case had actually been made by the purported signer. But that is not a fair reading of the question to which the agent was responding. As set out above, the grand juror’s question specifically referenced Count 37, which charged Bobka, Cavallo, and Horn-berger with making and causing to be made false statements in connection with a loan application submitted in Hornberger’s name. As the Government noted in its response to Defendants’ pretrial motion to dismiss the indictment, there was ample evidence to indicate that Hornberger had, in fact, signed this document. The Government’s contention is borne out by the fact that at trial, the jury found, beyond a reasonable doubt, that Hornberger was guilty of Count 37. And to the extent that the agent’s answer might arguably seem broader than just a reference to Count 37, it is apparent that he was not actually vouching for each signature on every document as, just minutes before this response, the agent had advised the grand jurors that Bobka had, in fact, forged Hornberger’s name on other documents. That the agent would thereafter immediately contradict his own testimony and assert that every signature in the case had been verified is implausible, as is the notion that the grand jury would so understand his testimony. In short, Defendants failed to demonstrate that the agent knowingly lied before the grand jury or that the prosecutor would understand the agent to have done so. The district court therefore did not err in denying the motions to dismiss the indictment. IV. ALLEGED EXTRINSIC INFLUENCE ON JURY Defendants Cavallo and Hornberger argue that their convictions should be reversed because, during deliberations, a juror allegedly went on the internet and learned that a testifying (and cooperating) co-conspirator had received only house arrest based on his conviction. Yet, because Defendants had obtained this information only as a result of Cavallo’s violation of a local rule forbidding contact with jurors, the district court struck the evidence that Cavallo offered in support of his allegation of extrinsic influence and denied Defendants’ motion for a new trial. In addition, the court concluded that the extrinsic information was not harmful to Defendants. We find no error in the district court’s decision. A. Background At the beginning of the sentencing hearing on October 26, 2012, the prosecutor informed the court that he had just observed Cavallo and Hornberger’s counsel, Ms. Unger, speaking with a juror from the trial in the hallway. Unger explained that the juror, Juror George, had approached her in the hallway and asked if they could speak. According to Unger, just as she was telling George that she could not talk to jurors, the prosecutor arrived on the scene. After hearing Unger’s explanation, the court addressed Juror George, who was present in the courtroom, and directed him not to communicate with anyone involved in the case. George confirmed that he understood the instruction, and the sentencing proceeded. On February 20, 2013, which was four months after the sentencing and over nine months after the jury had returned its verdict, Unger forwarded an email to prosecutors that she had received from Juror George that day. We summarize this single-spaced missive. The juror’s email begins with compliments for the good job that Unger had done at trial and an observation about the naiveté of fellow jurors,. who purportedly did not know how the justice system works and, in particular, that prosecutors “can be ruthless” and try “to paint the worst picture of the defendants.” George then reports to Unger that he has learned some “shocking” things and, in fact, had just spoken to Cavallo that very day. He notes that he believed that co-defendant Richard Bobka had been the cause of everyone’s “downfall.” Further, before finally voting to convict, George, along with another juror, had held out as long as they could, knowing that the “consequences of being convicted would be de-vistating [sic]” to the defendants. George explains that he had initially held out because he was not sure that the prosecution had proved its case beyond a reasonable doubt, but instead had only put up a “confusing smokescreen.” As to the female juror who had been holding out with him, she was hopeful that if she hung the jury, the Government would not retry the defendants. She was encouraged in this hope, having learned from the internet that one of the testifying co-conspirators who had pled guilty had received only house arrest. But George, who apparently by this time had decided to vote guilty on some counts, argued to this juror that the Government would not back - down and that, if convicted, the defendants would receive harsher sentences at a second trial. Eventually, the jury unanimously agreed to convict Defendants on one substantive count each, as well as on the conspiracy count. George closes the email by expressing his regret that he could not convince his fellow jurors to convict on just one count and also that they insisted on a conviction on .the conspiracy count, which he knew was “a bad one to get.” Finally, he advises Unger to feel free to contact him with any questions. Upon receiving this email from defense counsel, the Government filed a notice of juror communications with the district court, and Defendants moved for an evi-dentiary hearing to investigate potential juror misconduct. The court held an organizational meeting with the parties on March 7, 2013 and ordered all future proceedings in the matter to be sealed and all papers to be filed in camera. No one objected. The court also ordered the parties to submit questions for the court to ask Juror George, and all parties complied. On March 28, 2013, the court held the first of two in camera hearings. Government counsel, appellate counsel for each defendant, and Juror George and his appointed counsel were present. In response to some preliminary questions by the court, George testified that he had known the court was open to receiving messages from the jury, including during deliberations, and that if there had been a problem, he should have contacted the court, which he did not attempt to do at any point. He further testified that no juror attempted to discuss the case with him; no one provided him with any extrinsic evidence during trial; and he did not personally consult any outside sources or observe any other juror doing so. Regarding his encounter with defendant Cavallo and Cavallo’s attorney, Ms. Unger, immediately before sentencing, George testified that he had introduced himself to Cavallo, and Cavallo had returned his greeting. Then Unger told George that she wanted to talk to him and ask him questions, but they did not have an opportunity to talk further. George testified that although the hallway encounter was the only direct communication he had with Unger, four months later, in February 2013, he received a telephone call from Cavallo “out of the blue.” During that call, Cavallo told George that he had obtained George’s phone number from a newspaper reporter, Mike Braga, who had covered the trial. Cavallo also explained how devastating the conviction had been for him and his wife, co-defendant Horn-berger, noting that the Government was taking their family’s home, had “hit [their] bank accounts on Thanksgiving Day,” and was “going after everything they have.” Cavallo then asked George about the case and the jury’s deliberations, and George discussed that with him. George testified that Cavallo called him multiple times after the initial call. During one of those calls, Cavallo stated that he had spoken with Unger, and that Unger wanted George to email her about the jury deliberations. Cavallo gave Unger’s email address to George, and George emailed Unger, as Cavallo requested. Cavallo later called George to confirm that he had sent the email. During one phone call, George asked Cavallo why he had suddenly started receiving phone calls from a reporter named Braga, and Cavallo admitted that he had told Braga everything about the jury deliberations. George told Cavallo he was not comfortable with Bra-ga’s involvement and that he “did not want anything published.” Finally, George testified that he stood by the verdict rendered at trial. As noted, Defendants had made no objection when the district judge had announced, at the organizational meeting two weeks prior to the hearing, that she intended to “seal” the proceedings. Instead, they waited until the end of the hearing, to object, for the first time, to the proceedings being sealed and to Defendants themselves not being present. The district court ruled that Defendants had waived any objection to the proceedings being sealed. As to Defendants being present at any future hearing, the court instructed counsel to submit briefs if they wished to be present. Defendants filed no briefs. On April 9, 2013, the court conducted a follow up in camera hearing with the same parties present, and noted that Defendants had waived their objection to being present because they had failed to brief the issue, as directed by the court. As to evidentiary matters handled at this second hearing, Cavallo’s counsel offered Cavallo’s cell phone records to the court covering the dates on which Cavallo and George had communicated. The phone records reflected fewer communications between Ca-vallo and George than the latter had recalled in his testimony. These records showed that Cavallo sent one text message to George on February 19, and George sent one text message back that day. On February 20 and 21, George called Cavallo once, and Cavallo telephoned George twice. In short, the records revealed five communications between the two men: none of which had received prior court approval. After the court reviewed the phone records, the judge again questioned George, and the latter reaffirmed his earlier testimony that when he and Cavallo had spoken on the phone, they discussed the information that he subsequently put in the email to Unger concerning the jury’s deliberations. None of the defendants objected to the questions posed by the court, nor did they request that the court ask additional questions or call additional witnesses. Their earlier silence notwithstanding, over a week later, on April 19, 2013, Defendants filed an objection to the manner in which the court conducted its inquiry, and they moved to subpoena and question Braga, the news reporter, and the female juror who had allegedly conducted internet research. Defendants also argued for the first time that the court should have asked George more specific questions about the contents of his email. Albeit George had offered live testimony concerning his interactions with Unger and defendant Cavallo, the latter merely submitted affidavits containing their versions of their interactions with George. They made no request or offer to provide live testimony concerning their version of these events. Moreover, Unger’s affidavit was short and bereft of much detail, stating only that her sole exchange with George was on the day of the sentencing hearings, when George exited the elevator and greeted her, and that she neither instructed nor directed anyone to send the email she received from George. Unger never discussed whether she had conferred with Cavallo concerning the latter’s plan to contact George and the conversations between the two men. As to Cavallo’s affidavit, he stated that George approached him and Hornberger outside the courtroom at sentencing to introduce himself. Cav-allo sensed that George wanted to discuss something important, but they did not have an opportunity to speak further because Government counsel appeared. Cavallo was “haunted” by what George might have wanted to say to him, so “without anyone’s advice or encouragement,” he looked up George’s telephone number on Google, contacted a news reporter to obtain George’s email address, and then sent a text message to two of George’s telephone numbers on February 19. The next morning, Cavallo received a text message response from George and a phone call from George shortly thereafter. Cavallo stated that when he answered the phone, George, without solicitation, began to excitedly tell him about the things that took place during jury deliberations, including that a juror named Patricia looked up the sentence of Mike Bangasser, who had reportedly received only four months home detention. Then George asked for Unger’s contact information, and Cavallo gave George what he thought was Unger’s email address. George asked Cavallo to call him back to confirm Unger’s contact information, which is why Cavallo called George that afternoon. Cavallo admits that he encouraged George to call, write, or email anyone who might have had an interest in the proceedings but contends that he did not urge George to email Un-ger. Cavallo learned George had emailed Unger the next morning on February 21, and he called George that day to tell him that they could not speak again. After hearing and reviewing all this evidence, the district court issued an order in which it credited George’s sworn testimony about his encounters with Unger and Cavallo and concluded that the latter had violated the Middle District of Florida local rule restricting parties’ and attorneys’ contact with jurors, absent court permission. Indeed, as the court noted, despite Cavallo’s tepid efforts in his affidavit to discredit George’s testimony, the version of events presented in Cavallo’s affidavit actually supported George’s testimony that Cavallo contacted him “out of the blue” to discuss the case. As a sanction for violating Middle District of Florida Rule 5.01(d), which prohibits such party-juror communications, the court excluded George’s email against Cavallo and Hornberger, who are married and who were represented by the same counsel at trial. The court did not strike the email against Streinz because neither he nor his counsel were involved in the rule violation, but it found that any exposure of a juror to the extrinsic information alleged in the email, if such occurred, was not prejudicial to Defendants. Accordingly, the court denied all of Defendants’ requests for relief based on juror misconduct. B. Discussion Cavallo and Hornberger seek a reversal of their convictions based on the information about jury deliberations provided by Juror George in Cavallo’s conversations with George. To the extent that this information was insufficient to warrant the granting of a new trial, they also contend that the district court should have conducted a more thorough investigation of the alleged juror misconduct. We review the denial of a motion for new trial based on alleged juror misconduct for an abuse of discretion. United States v. Venske, 296 F.3d 1284, 1290 (11th Cir.2002). Finding no abuse of discretion, we affirm the district court’s denial of Defendants’ motion for a new trial. 1. Federal Rule of Evidence 606(b)’s Limitations on Judicial Inquiry Into Jury Deliberations “District courts are subject to very stringent limitations on their authority to question jurors about their deliberations,” and since 1915 “the Supreme Court has recognized a near-universal and firmly established common-law rule flatly prohibiting the use of juror testimony to impeach a verdict.” United States v. Siegelman, 640 F.3d 1159, 1185 (11th Cir.2011) (emphasis in original). Absent such a prohibition, “[j]urors would be harassed and beset by the defeated party in an effort to secure from them evidence of facts which might establish misconduct sufficient to set aside a verdict.” Id. at 1186 (quoting McDonald v. Pless, 238 U.S. 264, 267-68, 35 S.Ct. 783, 59 L.Ed. 1300 (1915)). To invalidate an undesirable verdict, allegations of juror misconduct would become commonplace and such scrutiny would discourage “full and frank discussions in the jury room, jurors’ willingness to return an unpopular verdict, and the community’s trust in a system that relies on the decisions of laypeople.” Id. at 1185 (quoting Tanner v. United States, 483 U.S. 107, 120-21, 107 S.Ct. 2739, 97 L.Ed.2d 90 (1987)). Therefore, in an effort to protect the integrity of the jury system and to forestall endless attacks on a jury’s verdict, the Federal Rules of Evidence have codified the common law rule against the admission of a juror’s testimony to impeach the jury’s verdict. Id. at 1186. Rule 606(b) provides: (b) During an Inquiry -Into the Validity of a Verdict or Indictment. (1) Prohibited Testimony or Other Evidence. During an inquiry into the validity of a verdict ... a juror may not testify about any statement made or incident that occurred during the jury’s deliberations; the effect of anything on that juror’s or another juror’s vote; or any juror’s mental processes concerning the verdict. ... The court may not receive a juror’s affidavit or evidence of a juror’s statement on these matters. (2) Exceptions. A juror may testify about whether: (A) extraneous prejudicial information was improperly brought to the jury’s attention; (B) an outside influence was improperly brought to bear on any juror; or (C) a mistake was made in entering the verdict on the verdict form. Fed.R.Evid. 606(b). In short, except for testimony concerning extraneous prejudicial information or improper outside influence, Rule 606(b)(1) prohibits a juror from providing testimony or other evidence about anything that happened or occurred during deliberations, including a juror’s mental processes or the reasons the jury reached a particular verdict. With only one exception, the infQrmation provided by George to Cavallo, and then to Cavallo’s attorney, was nothing but a description of the thought process of jury members—and mostly George’s own thought process— meaning this information was inadmissible to attack the jury’s verdict. The sole exception was George’s disclosure that a juror had learned from the internet that another co-conspirator who had pled guilty had received only house arrest and no jail time. Because this information was “extraneous,” and perhaps' prejudicial, Rule 606(b) does not prohibit a juror from testifying about it. Accordingly, the district court correctly ruled that it was only this last disclosure, to which we now turn, that was subject to scrutiny by the court. 2. Violation of Local Rule 5.01(d) by Defendants As noted, Rule 606(b) sets out a broad prohibition against questioning jurors about their deliberations or reasons for a particular verdict, with the exception that a juror may testify as to whether extraneous prejudicial information was improperly brought to his attention or outside influence was improperly exerted against him. There is no allegation of outside influence here, but Defendants have argued that their verdict should he vacated because the jurors received extraneous prejudicial information. As a general matter, information is deemed to be “‘extraneous’ if it derives from a source ‘external’ to the jury. ‘External’ matters include publicity, and information related specifically to the case the jurors are meant to decide.... ” Warger v. Shauers, 574 U.S. —, 135 S.Ct. 521, 529, 190 L.Ed.2d 422 (2014) (internal citations omitted). The district court, however, found it inappropriate to explore the allegedly “extraneous prejudicial information” that may have found its way to George or the female juror who initially wanted to hang the jury because Cavallo uncovered this information only by brazenly violating a local court rule that flatly forbade the contact that Cavallo made with George. We agree with the district court. Middle District of Florida Rule 5.01(d) (“Local Rule 5.01(d)”) restricts attorneys’ and parties’ contacts with jurors absent prior court approval. The rule provides: No attorney or party shall undertake, directly or indirectly, to interview any juror after trial in any civil or criminal case except as permitted by this Rule. If a party believes that grounds for legal challenge to a verdict exist, he may move for an order permitting an interview of a juror or jurors to determine whether the verdict is subject to the challenge. The motion shall be served within fourteen (14) days after rendition of the verdict unless good cause is shown for the failure to make the motion within that time. The motion shall state the name and address of each juror to be interviewed and the .grounds for the challenge that the moving party believes may exist. The presiding judge may conduct such hearings, if any, as necessary, and shall enter an order denying the motion or. permitting the interview. If the interview is permitted, the Court may prescribe the place, manner, conditions, and scope of the interview. To translate, neither an attorney nor a party may, directly or indirectly, attempt to interview a juror after trial unless.that person first obtains the court’s permission to do so. A motion seeking that permission must be filed within fourteen days after the verdict, absent a showing of good cause for a tardy filing. In addition, the motion must state not only the name of the juror to be interviewed, but also the basis for the request. In ruling on the motion, the district court is empowered to set limits on the scope or manner of the interview. Here, the district court concluded that Cavallo and, to some extent, Unger, engaged in conduct that violated this rule. As to the court’s conclusion regarding the conduct of these two, this is a factual finding that we reverse only if clearly erroneous. See United States v. Floyd, 281 F.3d 1346, 1348 (11th Cir.2002). Further, we accord great deference to a district court’s credibility determinations, United States v. Clay, 376 F.3d 1296, 1302 (11th Cir.2004), and we will not reverse a district court’s factual finding concerning credibility unless the finding is “contrary to the laws of nature, or is so inconsistent or improbable on its face that no reasonable factfinder could accept it.” United States v. Pineiro, 389 F.3d 1359, 1366 (11th Cir.2004) (quotations omitted). Here, the district court found to be truthful George’s testimony that Cavallo contacted George, engaged the latter in conversations about the jury’s deliberations, and told him that counsel Unger wanted George to email her with this information. The court also credited George’s testimony that Unger had told George at the time of the sentencing hearing that she would like to ask him questions. We do not find the district court’s conclusions on these matters to be clearly erroneous. Nor are we persuaded by Defendants’ argument that the district court should not have credited George’s testimony without first hearing directly from Cavallo and Unger, both of whom chose to file affidavits. If Cavallo or Unger wanted to testify, they should have asked to do so. Had Cavallo requested the opportunity to contradict George’s testimony with his own testimony, there is no reason to believe that anyone would have tried to stop him. Moreover, as noted supra, Cavallo has explained that he would not waive attorney-client privilege to allow Unger to testify, which suggests that Cavallo had his own reasons to be reticent about testifying on this matter and subjecting himself to cross-examination. Perhaps most significantly, Cavallo’s own affidavit confirms George’s testimony that it was Cavallo who initiated contact with George about jury deliberations. Defendants argue that, even if one accepts as true George’s testimony, Caval-lo’s exchange with George did not violate the local rule, as a legal matter. Specifically, Defendants argue that Local Rule 5.01(d) prohibits only the “interviewing” of a juror, but that it does not outlaw merely “communicating” with a juror, which they contend is all that Cavallo did. We give “great deference to a district court’s interpretation of its local rules,” Clark v. Hous. Auth. of City of Alma, 971 F.2d 723, 727 (11th Cir.1992), and we conclude that Ca-vallo’s argument fails to meet the straight-face test. Obviously, the only thing that George and Cavallo had in common was the trial where George served on the jury that found Cavallo guilty. Clearly, Cavallo was not interested in discussing the weather, politics, or sports with George. The jury’s deliberations were the only topic that would be of interest to him, and, in fact, it appears to be the only topic that the two men discussed. We find unpersuasive Cavallo’s parsing of the Local Rule’s description of the conduct that it prohibits, and we concur with the district court’s conclusion that Cavallo violated the rule. Finding no good reason to disturb the district court’s determination that Cavallo violated Local Rule 5.01(d), then the next question is whether the court’s striking of evidence procured only through Cavallo’s violation of the rule constituted a proper sanction for the latter’s breach. On this question, our precedent squarely supports the district court’s decision. In United States v. Venske, 296 F.3d 1284 (11th Cir.2002), a case which also arose out of the Middle District of Florida, two defendants sought a new trial before the district court, arguing that jurors had been exposed to prejudicial extrinsic information and supporting that contention with an affidavit that the court concluded they had obtained by violating the court’s local rule forbidding contact with jurors, absent prior court approval. Because the defendants had “knowingly and intentionally engaged in a scheme to defy the [local rule],” the district court excluded the affidavit and refused to conduct an evidentiary hearing on the allegation. Id. at 1289. We rejected the defendants’ argument challenging the power of a district court to enact a local rule restricting communications with jurors or to exclude evidence obtained in violation of such a rule. Id. at 1291. In affirming the d