Martin P. and Nanja Rutherford, who were found guilty of two counts of tax evasion, appeal the district court’s denial of their motion for a new trial on grounds of jury intimidation, tampering, and misconduct. They assert three errors on appeal. They first contend that the district court erred in concluding that jurors’ statements that they discussed Mrs. Rutherford failure to testify at trial were inadmissible under Fed.R.Evid. 606(b). We reject this contention and affirm the district court on this point. They also assert that the jury was prejudiced because a large number of IRS and government agents sat directly behind the prosecution table throughout the trial and glared at the jurors, intimidating them, and causing some of the jurors to fear that if they acquitted the Rutherfords, the IRS might retaliate against them. In this regard, the Rutherfords assert that the district court improperly restricted the scope of the evi-dentiary hearing and impeded their ability to make a prima facie showing that the jurors were adversely influenced by the government agents’ conduct. The Ruther-fords’ more fundamental contention, however, is that the district court erred in finding that théy must prove that the agents “intended” to influence the jurors. According to the ■ Rutherfords, they need show only that the agents’ conduct created a risk that the verdict might be influenced, regardless of the government’s motive. On the latter two points, we agree with the Rutherfords. Accordingly, we vacate the district court’s ruling, and remand for further proceedings.

a. The Underlying Tax Evasion Case

The IRS investigated the Rutherfords for filing false tax returns and not paying taxes, commencing with the 1988 returns. In 1999, after the Rutherfords failed to cooperate with an IRS agent investigating their 1992 and 1993 tax returns, the government charged them with willfully making and subscribing to a false income tax return, in violation of 26 U.S.C. § 7206 (1), and willfully failing to file an income tax return, in violation of 26 U.S.C. § 7203 (hereinafter “tax evasion”).

b. The Trial

The Rutherfords’ evidence at trial centered principally on proving that any underpayments in taxes were not intentional, but rather resulted from following inaccurate and misleading advice provided by individuals who held themselves out as tax experts. It was uncontested that, from 1969 until 1988, the Rutherfords paid their taxes in full without incident. However, between 1988 and 1990 they spent approximately $125,000 on Church of Scientology-related business courses and travel, an amount which they deducted from their returns. The IRS audited the couple’s returns for these years. It concluded that the Rutherfords had underpaid their taxes, largely on the ground that the deduction of the Scientology-related expenses was improper. The IRS auditor told the Ruther-fords that they owed approximately $150,000. Although the Rutherfords did not agree that they owed this amount, counsel advised them against contesting it due to the prohibitive costs of litigation.

Acting on counsel’s advice, Mr. Rutherford offered the IRS a settlement of $111,000 and sent a payment of $50,000 with the offer. The IRS accepted the offer and the payment.

Shortly thereafter, however, the IRS sent the Rutherfords a letter stating that they continued to owe $91,145.70. Mr. Rutherford testified that he was upset because he believed that he owed only $61,000 plus interest (the remainder of the $111,000 settlement). He said that he contacted an accountant to help resolve the discrepancy, but that, while he was on vacation, the IRS placed a levy on approximately $72,900 in his bank accounts.

After the IRS placed the levy on his bank account, Mr. Rutherford attended a seminar by Palle “Pono” Bognaes of International Tax Technology (“ITT”). Bog-naes claimed to be a tax specialist and attorney with 20 years experience. After a consultation with Bognaes, the Ruther-fords hired him to represent them and paid him approximately $18,000 in fees. The Rutherfords provided Bognaes with all the information regarding their 1992 taxes and relied on him to prepare a correct return. Bognaes advised the Ruther-fords that they owed no taxes for 1992 and, in fact, might be eligible for a refund.

Mr. Rutherford testified that he and his wife signed a blank tax form for their 1992 tax returns and gave it to Bognaes to fill out and file. Mr. Rutherford stated that it had been his common practice to sign blank returns when his bookkeeper had completed his taxes. He stated that he had “no evil intent” in filing the return, but rather was following the advice given by his representative. He testified that he received repeated assurances that everything Bognaes was recommending was legal.

Unsure about how to proceed in 1993, Mr. Rutherford hired a second tax attorney, Jerry Aurillo. Aurillo advised him not to file a tax return for 1993. Rutherford testified that he followed Aurillo’s advice.

The Rutherfords introduced expert testimony from Anthony Granata, a tax specialist. He opined that the Rutherfords were over-assessed taxes for 1988 through 1990, and therefore had approximately $62,500 in overpayments that they were entitled to carry forward to 1992 and 1993. He further testified that it was his opinion that, as a result of the carry forward of tax payments from previous years, if defendants’ tax obligation for 1992 was $70,000 (as the government contended), the amount of taxes of “zero” shown as due and owing on defendants’ filed return would be correct.

The government’s case centered on presenting evidence that the Rutherfords’ failure to include any income on their 1992 tax return and to file a 1993 tax return was willful. It introduced minutes from a November 20, 1992, meeting, which included the statement, “IRS: we have decided to fight back. Talked [sic] to the attorneys in Sacramento and find out if we have any recourse.” The IRS also presented evidence that, after it placed its levy on their bank accounts, the Rutherfords began shifting assets to an unincorporated business organization.

The Rutherfords’ former bookkeeper, Jo Niel, testified that in January of 1993, Mrs. Rutherford told her that she was “never filing taxes again.” Niel also testified that she told the Rutherfords that getting involved with Bognaes and ITT “wasn’t a good idea.”

The government introduced a statement made by Mrs. Rutherford in a May 28, 1993, management meeting: “Taxes, to pay or not to pay. That is a question all right, to be decided one way or another real soon.” It presented evidence that in February of 1993, Mr. and Mrs. Rutherford sent letters to the IRS, in which they stated that their wages were excluded from taxation by Congress. In February of 1993, Mrs. Rutherford also sent a letter demanding that the IRS stop withholding taxes from her wages. In another letter the Rutherfords asked that their signatures be canceled on all returns filed with the IRS between 1968 and 1991.

Mrs. Rutherford did not testify at trial. To ensure that the jury understood that it was impermissible to discuss or consider her failure to testify during its deliberations, the district court gave the following instruction:

The jury returned verdicts finding the defendants guilty on both counts. The court sentenced them each to five months imprisonment as to Count I, and five months imprisonment as to Count 2, to run concurrently, followed by one year of supervised release as to each Count, also to run concurrently. The court ordered them to pay restitution in the amount of $141,812.75 and costs of prosecution of $2,637. The court also ordered each of them to pay a fine of $3,999 and a special assessment of $75. The Rutherfords appealed and we rejected that appeal.

The Rutherfords then moved for a new trial, alleging that the jury had improperly discussed Mrs. Rutherford’s failure to testify and that the presence of so many IRS agents in the courtroom who were “glaring” at the jurors intimidated the jury and prejudiced its deliberations.

The Rutherfords introduced evidence that throughout the tax evasion trial, up to ten current and former agents of the IRS and Department of Justice (hereinafter “agents”) were in attendance. They also submitted affidavits of three jurors and one non-juror. The investigator who took the affidavits, Charles “Bo” Wiseman, stated that the affidavits were difficult to obtain because the jurors were “afraid of retaliation from the IRS.”

Juror Graham Hartung averred:

Hartung also stated that some of the jurors had discussed the power of the IRS.

Juror Vicki Walker averred:

Jury Foreperson Terry Hoff averred:

Non-juror Sandra Crow, a business associate of Russ Keele, another juror in the case, stated:

Two of the jurors also averred that they considered it significant that Mrs. Rutherford did not testify, and that the jurors discussed the matter during deliberations.

Juror Walker stated that,

Jury Foreperson Hoff also stated that,

After reviewing the affidavits, the district court concluded that the jurors’ statements relating to Mrs. Rutherford’s failure to testify were inadmissible under Fed. R.Evid. 606(b) and therefore that the Rutherfords’ claim that the jury did not follow the court’s instructions could not form a basis for a new trial.

In support of the allegations of jury intimidation or tampering, the district court struck portions of the jurors’ affidavits stating that they believed the IRS might retaliate against them, because such statements “constitute[d] evidence of the effect of such conduct upon jurors’ mind or emotions as influencing them to assent to or dissent from the verdict and[sic] concern jurors’ mental processes.” In the court’s view, the only statement that could provide a basis for the motion was Juror Walker’s statement regarding the presence of so many “glaring” IRS agents in the courtroom. Based on this statement, the court ordered an evidentiary hearing, but he expressly limited it to juror testimony as to “the existence of such [agent] conduct at the time it occurred.” He then advised the defendants that they bore the burden of proving that the government agents intended to intimidate or influence the jurors. Without such a showing, the judge concluded, the conduct must be considered as a more prosaic form of contact with the jurors, a form that would place the burden of proof on the defendants and require them to prove actual prejudice in order to obtain a new trial.

At the evidentiary hearing, it was established that between seven and ten agents of the IRS (and the Department of Justice), active and retired, were in the courtroom--throughout most of the- trial,- sitting in the first two rows behind the- prosecution table and, periodically, conversing with the prosecutors. Thé agents testified that théy attended the trial either as part of their duties or for training purposes, and that they did not attend with the purpose of intimidating the jurors.

At the end of the evidentiary hearing, the district judge found credible the testimony of a juror that agents sitting in the first and second row behind the prosecution had glared and stared at the jurors; he also noted that the jurors had discussed this fact among themselves on more than one occasion. According to the district judge, however, the issue was whether the government agents intended to intimidate or influence the jurors. He held that the Rutherfords had failed to prove that “[the conduct] of the IRS personnel was intentionally an effort to influence the jury. This means a knowing threat of some sort or other, an intentional act to influence the jury, a knowing and intentional act designed to influence the jury.” After finding that there was “no credible evidence that the IRS ... intended to [ ] influence the jury,” the court shifted the burden of proof to the defendants and required them to establish actual prejudice in order to be granted a new trial. Because the Ruther-fords could not prove “actual prejudice,” the court denied their motion for a new trial.

II.

The Rutherfords first contend that the district court erred in concluding that the jurors’ discussion of Mrs. Rutherford’s failure to testify was inadmissible.

Fed.R.Evid. 606(b) bars juror’s testimony as to “any matter or statement occurring during the course of the jury’s deliberations or to the effect of anything upon that or any other juror’s mind or emotions as influencing the juror to assent to or dissent from the verdict or indictment or concerning the juror’s mental processes in connection therewith.” Id. There are two exceptions: a juror may testify as to whether (1) “extraneous prejudicial information was improperly brought to the jury’s attention” or (2) whether “any outside influence was improperly brought to bear upon any juror.” Id.

Prior to this case, we have not addressed the specific issue presented here, namely whether Rule 606(b) bars consideration of jurors’ statements that they ignored the court’s instructions and discussed a defendant’s failure to testify during deliberations. However, in a somewhat analogous ease, United States v. Falsia, 724 F.2d 1339 (9th Cir.1983), we held that Rule 606(b) barred the admission of jurors’ statements that they had discussed the absence of a co-defendant and his failure to testify during deliberations. Id. at 1343 . In Falsia , the defendant sought a new trial because the trial judge refused to instruct the jury that the co-defendant was a fugitive, unavailable as a witness. The defendant presented declarations to support his motion in which the jurors admitted to being influenced by the co-defendant’s absence and failure to testify. Id. We held that the affidavits were inadmissible under Rule 606(b), because the jurors had learned of the co-defendant’s absence through observation during trial and related testimony, not as a result of the introduction of any outside “influences.” Id. Here, similarly, the jurors learned of Mrs. Rutherford’s failure to testify through their personal observations during trial, not through a prohibited route or improper ex parte contact. Under these circumstances, the district court did not err in concluding that testimony regarding Mrs. Rutherford’s absence from the witness stand is inadmissible under Rule 606(b) because, as in Falsía, it does not concern facts bearing on extraneous or outside influences on the deliberation. Id.

III.

The Rutherfords next contend that the district court erred in determining that where there are allegations of jury intimidation or tampering, prejudice should be presumed only if the defendants can prove that those whose actions are being challenged intended to influence the jury. Specifically, they assert that the district court erred in determining that, “regardless of the effect” the IRS agents’ conduct may have had on the jurors, without proof of intent on the agents’ part prejudice could not be presumed. They also contend that the district court erred in striking significant portions of the jurors’ affidavits on this basis and then limiting the scope of the matters to be pursued at the evidentia-ry hearing. They state that the district court’s error in this regard prevented them from developing a sufficient record showing that the agents’ conduct created a risk that the verdict would be influenced. Caliendo v. Warden, 365 F.3d 691, 698 (9th Cir.2004); United States v. Dutkel, 192 F.3d 893, 897 (9th Cir.1999). Because the two issues are intertwined, we address them together.

The Sixth Amendment “guarantees criminal defendants a verdict by impartial, indifferent jurors.” Dyer v. Calderon, 151 F.3d 970, 973 (9th Cir.1998) (en banc). To protect this right, in Mattox v. United States, 146 U.S. 140, 150, 151 , 13 S.Ct. 50 , 36 L.Ed. 917 (1892), the Supreme Court held that “[pjrivate communications, possibly prejudicial, between jurors and third persons, or witnesses, or the officer in charge, are absolutely forbidden, and invalidate the verdict, at least unless their harmlessness is made to appear.” Subsequently, in Remmer v. United States, 347 U.S. 227 , 74 S.Ct. 450 , 98 L.Ed. 654 (1954) (“Remmer I ”), the Court established that any “private communication, contact, or tampering, directly or indirectly, with a juror during a trial about the matter pending before the jury” is deemed “presumptively prejudicial” and placed a heavy burden on the government to rebut the presumption by proving that the error was harmless beyond a reasonable doubt. Id. at 229 , 74 S.Ct. 450 ; see also United States v. Henley, 238 F.3d at 1118 (stating that once, the presumption applies the government must demonstrate that “there is no reasonable possibility that [a juror] was affected in his freedom of action as a juror” as to defendants) (internal quotations and ellipses omitted). The importance of the application of the presumption cannot be overstated. Where a juror is improperly contacted during a trial, “the potential for prejudice ... is significant” but it is often “very difficult for the defendant to prove.” United States v. Harbin, 250 F.3d 532 , 544 (7th Cir.2001).

In Remmer v. United States, 350 U.S. 377, 382 , 76 S.Ct. 425 , 100 L.Ed. 435 (1956) (“Remmer II ”), the Court suggested that only “unauthorized intrusions” into the “sanctity of the jury’s right to operate as freely as possible” purposefully made might trigger the presumption of prejudice. Id. at 382 , 76 S.Ct. 425 . Shortly thereafter, however, in a case in which intent was admittedly lacking, the Court clarified the issue, holding that the “fact that the intrusion was unintentional does not remove the effect of the intrusion.” Gold v. United States, 352 U.S. 985 , 77 S.Ct. 378 , 1 L.Ed.2d 360 (1957) (per cu-riam) (emphasis added) (citing Remmer II, reversing and remanding the case to the district court with directions to grant a new trial). In Gold , an FBI agent, investigating another case involving the falsity of a non-Communist affidavit, “accidentally]” contacted three members of the jury during the trial and inquired as to whether they had received any “propaganda” literature. Id. at 986 , 77 S.Ct. 378 (Reed, J., dissenting). Although the FBI agent’s conduct was not intended to influence the jurors (and the parties agreed that the solicitation was accidental), the Court applied Remmer II and held that a new trial was required. Id. at 985 , 77 S.Ct. 378 ; see also Remmer I, 347 U.S. at 229 , 74 S.Ct. 450 (“A juror must feel free to exercise his function without ... anyone else looking over his shoulder. The integrity of jury proceedings must not be jeopardized by unauthorized invasions.”).

We have applied the Remmer/Mattox rule in a number of cases and have consistently stated that the appropriate inquiry is whether the unauthorized conduct or contact is potentially prejudicial, not whether the parties alleged to have tampered with the jury did so intentionally. See, e.g., Caliendo, 365 F.3d at 697 (stating that the presumption of prejudice applies when the unauthorized conduct or contact is possibly prejudicial); Henley, 238 F.3d at 1117 (stating that the presumption of prejudice applies upon a showing that the “intrusion interfered with the jury’s deliberations by distracting one or more of the jurors”) (internal quotations omitted). In United States v. Angulo, 4 F.3d 843, 846 (9th Cir.1993), we recognized that in order to determine whether the jury might have been prejudiced, it may be necessary to inquire into the jurors’ perceptions of the conduct and any effect the conduct may have had on their ability to remain impartial and unbiased. In Angulo , a juror received an anonymous call, in which the caller stated, “I know where you live.” Id. The juror informed her fellow jurors of the call and also told the judge about the incident. The judge excused the juror; however, he refused to order a mistrial. Id. We reversed and directed the district court to conduct an evidentiary hearing, holding that “[u]nder these facts, the remaining jury members may well have believed that defendants were responsible for the threat and, based on that assumption, may have decided the merits of the case on that basis.” Id. at 847 (emphasis added). Because there was no evidence either that anyone associated with the defendants had placed the call or that the call, which might well have been a harmless prank, was intended to influence the juror, let alone the other jurors, our decision was necessarily based on the jurors’ perceptions of the conduct at issue and not on the “intent” of the caller.

Similarly, in Dutkel, 192 F.3d at 897 , we held that, in determining whether the defendant had made a prima facie showing of jury tampering, thereby triggering the presumption of prejudice, the relevant inquiry is whether the intrusion had an adverse effect on the deliberations. To give meaning to the term “adverse effect,” we instructed that in determining whether there was a possibility of prejudice a court should consider “whether the intervention interfered with the jury’s deliberations by distracting one or more of the jurors, or by introducing some other extraneous factor into the deliberative process.” Id. Because, in Dutkel , the juror’s concerns resulting from improper contacts might well have “prevented[him] from thinking about the evidence or paying attention to the judge’s instructions,” id. at 898 , we held that a prima facie case had been established, which triggered the presumption of prejudice.

Further, in United States v. Elias, 269 F.3d 1003 (9th Cir.2001), in determining whether the presumption of prejudice should apply, we again looked not to the intent of the individual alleged to have tampered .with the jury, but rather to the jurors’ perceptions of the conduct at issue. In Elias , after the verdict was entered, the trial judge learned that the defendant had approached a juror and asked her what it would take to buy her off. Id. at 1019 . The judge presumed that the contact was prejudicial and immediately held an evi-dentiary hearing. Id. At the hearing, the jurors testified that they believed that the defendant had made the comments in jest. Id. at 1019 . They informed the court that the alleged remarks did not scare them or distract them from listening to the evidence and that they were able to remain fair and impartial in the case. Id. at 1020 . We concluded that the district court conducted an appropriate inquiry. ' Id. Again, the inquiry in Elias was centered not on whether the defendant had intended to bribe the jurors — the defendant was not called to testify about his intent in making the comments — but on the jurors’ perception of the defendant’s conduct, i.e. whether they believed he was joking or serious and whether the defendant’s conduct had scared or distracted them. Id. at 1020 . Thus, it is clear from our precedent that when considering possible incidents of jury tampering or intimidation, “we are ultimately not so concerned with their nature as with the prejudice they may have worked on the fairness of the defendant’s trial.” United States v. Armstrong, 654 F.2d 1328, 1332 (9th Cir.1981). Accordingly, in cases in which the circumstances suggest that the improper communication or contact is sufficiently serious that.it might prejudice the jurors we have afforded the presumption of prejudice; in the case of other more “prosaic kinds of jury misconduct” we have not. Henley, 238 F.3d at 1116 (discussing the difference); see also Dutkel, 192 F.3d at 894 (discussing the difference); Angulo, 4 F.3d at 848 n. 7 (same).

In this case, the conduct at issue was that of government agents intimately associated with the prosecution. The IRS and DOJ agents sat directly behind the prosecution table throughout the trial, several of the agents were key witnesses in the case, and the prosecutor turned around and conversed with the agents during the trial proceedings and trial breaks. At least one juror alleged that a number of the agents regularly glared at her and her fellow jurors. The courts have emphasized that judges should exercise additional caution when government employees are involved, because of a heightened concern that the jurors will not “feel free to exercise [their] functions” with the Government “looking over [their] shoulder[s].” Remmer I, 347 U.S. at 229 , 74 S.Ct. 450 ; see also United States v. Brande, 329 F.3d 1173, 1178 (9th Cir.2003) (stating that special duty of judges to ensure impartiality of the jury is “heightened when a potential breach of impartiality may have resulted from the act of a court employee”). Because of the perceived, as well as actual, power that government actors have at their disposal and the positions of authority that they occupy, we have held that even seemingly innocuous juror conversations and contact between such individuals and a juror can trigger a presumption of prejudice.

For these reasons, we hold that the district court erred in concluding that the defendant must prove that the individuals involved intended to influence or prejudice the jurors in order for the presumption of prejudice to apply. The appropriate inquiry is whether the unauthorized conduct “raises a risk of influencing the verdict,” Caliendo,' 365 F.3d at 697 , or “had an adverse effect on the deliberations,” Henley, 238 F.3d at 1115. However, because, as we discuss below, we also conclude that the district court erred in limiting juror testimony at the evidentiary hearing to “the existence of such conduct at the time it occurred,” it would not be appropriate for us, on this incomplete record, to determine whether the presumption should apply and whether the jurors were adversely influenced by the agents’ conduct at the trial. Rather, we leave that task to the district judge following the holding of a further evidentiary hearing.

Although the line that courts have drawn between the forms of juror testimony that are admissible and even inadmissible to show juror bias is imprecise — and although some may consider it artificial— we have made it clear that a court may not, under Rule 606(b), consider testimony “regarding the affected juror’s mental processes in reaching the verdict.” Elias, 269 F.3d at 1020 (citing Henley, 238 F.3d at 1118) (emphasis added). Thus, for example, a juror cannot testify to whether an outside influence caused him to change his vote from innocent to guilty. However, a court can and should consider'the “effect of extraneous information or improper contacts on a juror’s state of mind,” a juror’s “general fear and anxiety following” such an incident, and any other thoughts a juror might have about the contacts or conduct at issue. Id. In this regard, a juror’s testimony concerning his fear that individuals would retaliate against him if he voted to acquit (or convict) would be admissible, although his statement that he actually cast his vote one way or the other because of that fear would not. See Dutkel, 192 F.3d at 898 (considering evidence that, because of the improper contacts, the juror was “a disturbed and troubled man, deeply concerned about his own and his- family’s safety”) (internal quotations omitted). Further, evidence regarding any influence that such improper conduct or contacts had on the jurors’ abilities to fairly and impartially receive the evidence, listen to the testimony presented, and' the judge’s instructions is also admissible. Compare Elias, 269 F.3d at 1021 (finding no juror bias because both jurors testified that the defendant’s comments were in jest and that they “did not preoccupy them at the time, frighten them, or distract them from focusing on the evidence”), with Henley, 238 F.3d at 1117 (stating that because juror’s concerns may well have prevented him- from “thinking about the evidence or paying attention to the judge’s instructions,” the presumption of prejudice should apply) (internal quotation omitted). Final ly, the court may consider the likely consequence of actions that might cause jurors to feel intimidated regardless of whether the jurors admit such an effect. Thus, objective and subjective factors may both be considered.

In view of the above, we agree with the Rutherfords that the district court erred in limiting juror testimony to “the existence of [IRS] conduct at the time it occurred.” On remand, the district court should allow the parties to introduce evidence regarding the jurors’ perceptions of .the agents’ conduct and any discussions among the jurors concerning the possibility of IRS retaliation if they voted to acquit. See Henley, 238 F.3d at 1117 (stating that testimony “regarding a juror’s more general fear and anxiety following a tampering incident ... is admissible for the purposes of determining whether there is a reasonable possibility that the extraneous contact affected the verdict.”) (internal quotation omitted). After reviewing the evidence, if the court determines that the agents’ conduct raised a risk of influencing the verdict, then the presumption of prejudice should be applied.

In sum, because the district court applied the wrong legal standard and improperly limited the scope of the eviden-tiary hearing, we vacate and remand for further proceedings consistent with this opinion. If upon completion of those proceedings, the district court concludes that the verdict was tainted, the judgment of conviction shall be set aside and a new trial may be conducted, if the prosecution so elects. Should, however, the district court determine that no jury intimidation or tampering occurred, it shall reinstate the judgment.

VACATED AND REMANDED.

. Despite his representations, Bognaes was not a licensed attorney. . Mr. Rutherford also testified that he received several notices from the IRS that informed him that he had overpaid taxes in previous years, and that these overpayments had been applied to other taxes owed. He stated that, at the time, he believed the overpayment notices were related to his income taxes. At trial, he recognized that it was his employment taxes that he had overpaid. . In their first appeal, the Rutherfords raised several issues regarding the district court’s various evidentiary rulings and its failure to grant their Fed.R.Civ.P. 29 motions for judgments of acquittal, none of which is the subject of the current appeal. The court affirmed their convictions in a memorandum disposition. United States v. Rutherford, 39 Fed. Appx. 574 (9th Cir.2002). The present appeal is from the denial of the new trial motion made pursuant to Fed.R.Crim.P. 33(b)(1). . The other circuits that have addressed this question have held, as we do here, that because the juror did not learn of the defendant's failure to testify through improper channels, jurors' discussions regarding this fact do not fall within either exception of Rule 606(b)’s. See, e.g., United States v. Tran, 122 F.3d 670, 672-73 (8th Cir.1997) (holding that discussions of defendant’s failure to testify were "not 'extraneous' [prejudicial] 'information,' and therefore did not fall within the exception outlined in Rule 606(b)”) (alteration in original); United States v. Voigt, 877 F.2d 1465, 1469 (10th Cir.1989) (same); United States v. Friedland, 660 F.2d 919, 927-28 (3d Cir.1981) (same); United States v. Martinez-Moncivais, 14 F.3d 1030, 1036 (5th Cir.1994) (holding that post-trial statements that juror believed that if the defendant had been innocent, he would have taken the stand, did not fall into the "narrow exception that arises when there is evidence of outside influences on the jury”). . The government points to our statement in Dutkel that jury tampering is "normally understood” as “an effort to influence the jury’s verdict by threatening or offering inducements to one or more of the jurors.” Id. at 895. We stand by that statement. What we described in Dutkel is certainly the case in many, if not most, instances of jury tampering. However, Dutkel did not purport to describe all cases of jury tampering;; nor did it consider the question presented here. We do not read Dutkel’s generic description of jury tampering as limiting the application of the presumption of prejudice to only those cases in which it can be shown that there was an intent to prejudice the jury, particularly because, in Dutkel , we reaffirmed the reasoning in Angulo and stated that "even indirect coercive contacts that could affect the peace of mind of the jurors give rise to the Remmer presumption.” Id. at 897. . See Turner v. Louisiana, 379 U.S. 466, 472-73 , 85 S.Ct. 546 , 13 L.Ed.2d 424 (1965) (granting a new trial because the jurors had inappropriate contact with key witnesses (police officers) for the prosecution); Caliendo, 365 F.3d at 692 (granting habeas relief where three deliberating jurors chatted amiably and at length with the critical prosecution witness, a police officer, in an uncontrolled setting); United States v. O’Brien, 972 F.2d 12, 13-15 (1st Cir.1992) (upholding a guilty verdict but applying a presumption of prejudice where a police officer who was a potential prosecution witness, but who did not testify, spoke with three jurors during a recess about matters unrelated to the case, and stating that "any unauthorized communication between any person who is associated with the case, or who has an interest in the outcome of the case, and a juror would have the potential for being prejudicial”); United States v. Betner, 489 F.2d 116, 117-19 (5th Cir.1974) (ordering a new trial because the prosecutor conversed with the jury panel during a recess and the trial court failed to conduct an adequate hearing); see also Parker v. Gladden, 385 U.S. 363, 363-64 , 87 S.Ct. 468 , 17 L.Ed.2d 420 (1966) (per curiam) (holding that the impartiality of the jury was tainted when a court bailiff expressed to a juror his personal opinion that the defendant was guilty). . While we express no opinion as to the merits on remand, it is clear that, standing alone, the mere attendance of seven to ten agents at trial is not grounds for applying a presumption of prejudice, or, for that matter, granting a new trial. Glaring and staring at jurors on a regular basis may be another matter. . In this regard, we note that jurors are often reluctant to disclose whether they were influenced by an improper contact. Cf. Jeffries v. Wood, 114 F.3d 1484, 1491 (9th Cir.1997) (en banc) (stating that the prejudicial effect of an extrinsic contact "may be substantial even though it is not perceived by the juror, and a juror's good faith cannot counter this effect”) (internal quotation omitted); United States v. Barfield Co. Inc., 359 F.2d 120, 124 (5th Cir.1966) (stating that juror's testimony that he was not influenced by a conversation he had with one of the parties about non-trial related matters, was not dispositive because "it would no doubt be difficult to have a juror admit that he was influenced by such an approach.”).