In need of quick cash to satisfy his heroin addiction, defendant-appellant Michael Davis sold a .12 gauge sawed-off shotgun to Debra Schwede, a paid informant assisting in a Bureau of Alcohol, Tobacco, and Firearms investigation. A jury convicted Davis of possession of a non-registered firearm in violation of 26 U.S.C. § 6861(d) and possession of a firearm by a felon in violation of 18 U.S.C. § 922(g)(1), but acquitted him of transferring a firearm in violation of 26 U.S.C. § 6861(e). The district court sentenced Davis to 33 months of imprisonment to be followed by three years of probation (supervised release). On appeal, Davis contends 1) the evidence in support of the two possession convictions was insufficient, 2) certain remarks made by the prosecutor during closing argument denied him a fair trial, 3) the jury selection process was improper, and 4) the government engaged in outrageous conduct. We affirm.
BACKGROUND
Davis’s convictions arose out of “Operation Triggerlock,” an ATF investigation designed to rid a Chicago, Illinois west-side neighborhood of illegal weapons sales. As part of the operation, the ATF employed Schwede, a neighborhood local, and had her accompany John Rotunno, an ATF special agent posing as her drug-dealing, weapons-buying Californian brother.
Schwede testified that on June 11, 1990, while she stood next to a hot dog stand, Davis pulled up and asked her if her “brother was still interested in that.” By “that,” Schwede assumed Davis meant guns because, as Schwede testified, “everyone on the west side knew that my brother was buying guns.” After telling Davis her brother was still interested, Davis replied that he had a gun he wanted to sell. After Davis departed, Schwede consulted with her ATF contacts and made plans to purchase the weapon.
Two days later, Schwede, carrying a concealed tape recorder furnished by the government, went to Davis’s home. Davis, after greeting Schwede and inviting her into his home, retrieved a sawed-off shotgun from a closet, wrapped it in Christmas paper, and gave it to her. Schwede handed Davis $250, placed the wrapped gun in a bag, and departed.
At trial, Davis readily admitted he sold the sawed-off shotgun to Schwede, but claimed he was entrapped into illegally possessing as wéll as entrapped into illegally selling the weapon. He testified that in October of 1989 he inherited a house — with a full-barreled shotgun in it — from his deceased father. After hearing Schwede repeatedly make known her.brother’s desire to buy sawed-off shotguns, Davis stated he finally gave in and used a hacksaw to saw off the shotgun’s barrel; as he put it, “I just grabbed a hacksaw and went at it.” Davis testified that upon receiving the $260, “I ran straight out of the house and went to get me some heroin.” He claimed that both his severe heroin addiction and Schwede’s cpnstant hounding him for the gun induced him to shorten the barrel and sell the weapon for quick cash.
DISCUSSION
I. Sufficiency of the Evidence
Davis contends the evidence presented at trial was insufficient to establish his guilt beyond a reasonable, doubt on both possession counts. Count I charged Davis with being a felon in possession of a firearm, in violation of 18 U.S.C. § 922(g)(1), and Count II charged him with possessing a non-registered firearm, in violation of 26 U.S.C. § 5861(d).
When reviewing challenges to the sufficiency of evidence supporting a conviction, we consider the evidence presented at trial in the light most favorable to the government; if we conclude that any rational trier of fact could have found that the essential elements of the crime were proven beyond a reasonable doubt, we will reject the defendant’s sufficiency challenge. Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 2789, 61 L.Ed.2d 560 (1979). The reviewing court neither weighs the evidence nor assesses the credibility of witnesses, “even when the evi*1398dence at trial is ‘totally uncorroborated and comes from an admitted liar, convicted felon, large-scale drug-dealing, paid government informant’[.]” United States v. Beverly, 913 F.2d. 337, 358 (7th Cir.1990), cert. denied, 498 U.S. 1052, 111 S.Ct. 766, 112 L.Ed.2d 786 (1991) (citing United States v. Molinaro, 877 F.2d 1341, 1347 (7th Cir.1989)).
Count I: Felon in Possession of a Firearm
Davis challenges the sufficiency of the evidence under Count I, which charged him with being a felon in possession of a .12 gauge sawed-off shotgun transported in interstate commerce, in violation of 18 U.S.C. § 922(g)(1). Davis stipulated that he is a convicted felon (having been convicted of the sale of a stolen treasury check and possession of stolen mail on June 20,1989) and does not dispute the fact that the gun he sold is classified as a “weapon” under the statute 18 U.S.C. § 921(a)(3)(A). Neither does Davis challenge the government’s evidence that the gun was transported in interstate commerce.
It appears Davis’s sole challenge to the sufficiency of this particular conviction relies on his assertion that the government entrapped him into removing the gun from his closet and selling it to Schwede. He insists he had not removed the gun from the closet since receiving it, except to shorten the barrel and sell the weapon to Schwede. But Davis ignores the fact that he accepted the shotgun from his father’s estate and kept the shotgun in his closet in his house. By keeping the weapon in his immediate occupancy and control, the convicted felon was in actual possession of the weapon in violation of federal law. Actual possession “exists where the thing is in the immediate occupancy and control of the party.” BLACK’S LAW DICTIONARY 1047 (5th ed. 1979). Davis’s own testimony conclusively shows he actually possessed the firearm from the moment he inherited it. On. cross-examination, Davis testified as follows:
Q. Where was the gun all that time?
A. In the house.
Q. And that’s your house, correct?
A. Right.
Q. You were prohibited from having any guns. The law did not allow you to have any guns, correct?
A. Yes.
Q. But yet you had that?
A I — well, it was something that I had inherited, you know. It’s just [the] same as an old suit, man, you know. If someone’s giving it to you, it has sentimental value to you.
Q. So you kept it?
A. Well, I took it from — well, I kept it from people that could get in possession of it, yeah.
Q. So you kept it?
A. Well, yes.
Q. And no one induced you to keep it. You kept it because you wanted to keep it, correct?
A. No. Well, yeah.
Q. You had the gun, kept the gun, prior to even having the conversation with [Schwede], isn’t that correct?
A. The gun was in the house.
Not only does substantial evidence of probative value support Davis’s conviction under 18 U.S.C. § 922(g)(1) beyond a reasonable doubt, it supports the conviction beyond all doubt, literally. Davis’s own stipulations and his own testimony proved he possessed the firearm conclusively. We therefore reject Davis’s sufficiency challenge to his conviction of being a felon in possession of a firearm.
Count II: Possession of a Non-Registered Firearm
Neither do we find persuasive Davis’s argument that the evidence presented was insufficient to support his conviction under Count II, possessing a non-registered firearm. 26 U.S.C. § 5861(d) makes it unlawful for an individual “to receive or possess a firearm which is not registered to him in the National Firearms Registration and Transfer Reeord[.]” For purposes of § 5861(d), a “firearm” is defined, in part, as “a shotgun having a barrel or barrels of less than 18 inches in length.” 26 U.S.C. § 5845(a). Davis stipulated that his shotgun was not registered, and it is undisputed that the shot*1399gun he sold to Schwede had a barrel measuring less than 18 inches in length.
Davis maintains that he reduced the barrel to less than 18 inches in length only because he was entrapped into shortening the barrel by Schwede’s urging him to sell her brother a sawed-off shotgun. Davis testified that he sawed off the barrel with a hacksaw shortly before the June 11th, 1990 sale because he needed quick cash to satisfy his heroin addiction. The jury, however, was not required to — and obviously did not — believe Davis’s entrapment defense. Rather, the jury’s guilty verdict demonstrates it believed ATF special agent Mark Bartholomew, who testified that based on the wear and rust exhibited at the point where the barrel was cut, the barrel had been sawed off for quite a period of time, “probably four or five years.”
The jury’s acquittal of the illegal transfer charge (Count III) is of no consequence to our analysis. Even if the jury believed that the government entrapped Davis into selling the gun, it does not necessarily follow that the jury would come to the conclusion that the government also entrapped Davis into shortening the barrel. It was entirely possible — indeed, it was proven — that Davis either inherited the gun with its barrel sawed off or that Davis or someone else shortened the barrel some years before the sale and his arrest. In either scenario, it is immaterial who shortened the barrel, for Davis was not charged with shortening the barrel, but with mere possession of a sawed-off shotgun. There is no question he possessed the shotgun with a barrel less than 18 inches in length, and the jury rejected his argument that he shortened the barrel just prior to the sale because he was entrapped into doing so. As pointed out above, we will not reweigh conflicting evidence (when the gun’s barrel was shortened) and substitute the version the defendant prefers for that reached by the jury. Because the evidence that the felon Davis possessed an unregistered firearm in violation of 26 U.S.C. § 5861(d) is overwhelming, we reject this sufficiency of the evidence challenge as well.
II. Comment on Witness’s Truthfulness
Davis next contends that because certain remarks made by the prosecutor during closing argument denied him a fair trial, the district court erroneously denied his motion for mistrial. We review a trial court’s disposition of a mistrial motion under an abuse of discretion standard; the judge was present, throughout the trial and was in the best position to determine the seriousness of any allegations or acts of questionable conduct occurring during the trial. United States v. Henry, 2 F.3d 792, 794 (7th Cir.1993).
A.
During closing argument, Davis’s attorney relentlessly attacked Debra Schwede’s credibility, arguing that she was unreliable because she both purchased and used drugs and then lied about it. A sampling of Davis’s attack on Sehwede’s credibility follows: There are a whole bunch of things that she lied about. It is clear that she lied about.
Let’s talk about some of the lies that she had. I had to write them down, too many to remember. Okay. She stood up there under oath, and she denied that she was ever told by any of the agents that she should attempt to buy sawed-off shotguns. ... So that was a lie, ladies and gentlemen. But that’s not the only lie she told up .there. She lied about her drug use. Is that credible that this woman never used drugs? Oh, she used marijuana a long time ago ... but no, I never use drugs, not me.' Does that make any sense? Is that credible to you?
On top of that she lied to the grand jury under oath.... She lied to the grand jury. She doesn’t care about lying under oath. That’s what she gets paid to do, ladies and gentlemen. That what she does, anyway.
* * * * * *
Just like the oath she took to the grand jury, and. she got up and lied to them. And just like the oath she took here, she got up and lied to all of us.
It’s just like I told you in opening statement, we have got an informant who is out *1400of control. The agents are not able to control her.
Faced with this vicious attack on Schwede’s credibility, the prosecutor exercised Davis’s open invitation to address the issue of Schwe-de’s credibility. In rebuttal, the Assistant United States Attorney replied,
Ladies and gentlemen of the jury, was Debra Schwede a drug user? Absolutely not. You heard the agents tell you that their life was at stake in that case. They were not going to use someone as a [confidential informant] who would put their life in jeopardy on the West Side of Chicago. It didn’t happen.
Now, did Debra Schwede beforehand, before she became a [confidential informant], did she have to buy drugs for her boyfriend? She did that. And you think about it, ladies and gentlemen, she didn’t lie to you about that. She did not deny that it happened because she has to tell the truth. We will not use her otherwise. Those agents lives were in jeopardy if they had someone that used drugs. Simply it is not going to happen. You don’t do that. It is not that important. You don’t put your life in the hands of someone like that who is not reliable.
Davis objected to the prosecutor’s statements, claiming they amounted to vouching for the truthfulness of Debra Schwede’s testimony. The judge overruled the objection by saying, “I interpreted the statement to refer to the testimony of Agent Rotunno who said that he cheeked his people out and determined that they were reliable and wouldn’t use them if he didn’t think they were.... In any case, I think there was no prejudice^]” The district court later instructed the jury as follows:
Closing arguments of counsel are for the purpose of discussing the evidence.... The evidence consists of the sworn testimony of the witnesses, the exhibits received in evidence, and stipulated or admitted facts.... You are to consider only the evidence received in the case[.]
* * * * * *
You have heard testimony that the informant Debra Schwede has received benefits from the government in connection with this case, including cash payments and no prosecution for the delivery of illegal drugs. You may give her testimony such weight as you feel it deserves keeping in mind whether the testimony of this witness has been influenced by the benefits she has received from the government.
******
You are the sole judges of the credibility of the witnesses and of the weight to be given to the testimony of each of them.
Characterizing Schwede as the government’s “key witness” and her testimony as “crucial,” Davis complains the prosecutor’s vouching for Schwede’s truthfulness denied him a fair trial and entitled him to a mistrial.
We agree with the district court that the prosecutor’s remark was in reference to Agent Rotunno’s earlier testimony that he (Rotunno) always investigated his informants before using them to make sure they were reliable and that he would not use an unreliable person as an informant. It is permissible for a prosecutor to “comment upon what the evidence showed[,]” United States v. Auer-bach, 913 F.2d 407, 418 (7th Cir.1990), and in this case the evidence showed that Agent Rotunno had testified that he was careful about whom he used as an informant. Moreover, we observe that the prosecutor’s remarks were in direct response to the attack Davis launched on Debra Schwede’s credibility; in other words, as discussed below, the remarks were invited. Having launched the attack on Schwede’s credibility — and by implication, on Agent Rotunno’s professional judgment, Davis is in a poor position to claim that the response to his attack denied him a fair trial. We note that the prosecutor responded to the attack at the earliest opportunity, on rebuttal. But despite the fact that the prosecutor’s comments were invited and merely commented on the evidence presented, the remarks might conceivably be interpreted as a statement of the prosecutor’s personal opinion concerning Debra Schwe-de’s truthfulness.
We all realize it is never proper for any attorney to vouch for the truthfulness of a witness’s testimony because the determina*1401tion of credibility is a task left exclusively to the jury. After calling Schwede as a witness, the prosecutor’s statement that the government would not use her if she were not truthful may have appeared to amount to a vouching for Schwede’s truthfulness,- even in the context of rebutting Davis’s attack. When vouching occurs, however, it does not always require reversal becausé vouching does not necessarily deny a defendant a fair trial. To determine whether vouching requires a new trial,
we [first] evaluate the remark in light of the entire trial and determine whether it deprived the defendant of a fair trial. Five factors influence our evaluation of the impact of a prosecutor’s improper comment: (1) the nature and seriousness of the prosecutor’s misconduct; (2) whether the prosecutor’s statements were invited by impermissible conduct of the defense counsel; (3) whether the trial court instructed the jury to disregard- the statements; (4) whether the defense was able to counter the improper arguments through rebuttal; and (5) the weight of the evidence against the defendant.
Henry, 2 F.3d at 794 (citations omitted).
After reviewing the record and considering these five factors we are convinced that comment does not warrant reversal. With regard to Count I, felon in possession of a firearm, while it may be true that without Sehwede’s assistance Davis would not have been arrested and charged, it was established at trial beyond a reasonable doubt that Davis illegally possessed the sawed-off shotgun even before his involvement with Schwe-de. Davis admitted he had kept the gun in his closet from the moment he inherited it, that he was a convicted felon, that the weapon had been transported in interstate commerce and was not registered in the National Firearms Registration and Transfer Record, and that when he sold the weapon its barrel was less than 18 inches in length. By his own admissions, Davis established his guilt under 18 U.S.C. § 922(g)(1) (felon in possession of firearm). As to the conviction under Count II for possession of an unregistered' firearm pursuant to 26 U.S.C. § -5861(d), the jury did the rest by finding that based on the existence and degree of wear and rust at the point where the barrel was cut, the barrel had been shortened long before Davis sold the weapon to Schwede.
Any question as to Sehwede’s truthfulness really is not an issue in relation to Davis’s two convictions for possession, except to the extent that Schwede was involved in and assisted the officers in the investigation prior to Davis’s arrest'. As we mentioned earlier, Schwede’s truthfulness' was relevant only to the count charging Davis with illegally transferring the sawed-off shotgun to Schwede, but the jury acquitted Davis of that issue. Davis’s reliance upon United States v. Di Loreto, 888 F.2d 996 (3d Cir.1989), in which the court reversed the conviction based on improper vouching, is misplaced because in that case the witness’s credibility was “crucial.” Id. at 1000. In sum, for purposes of proving the two possession counts, it was Davis who was the key witness, not Schwede.
Second, as we pointed out above, the prosecutor’s remarks were an RSVP to the defendant’s invitation to address the issue of Schwede’s credibility and were limited to that topic. • “We have held that;' where defense counsel ‘struck the first blow5 by impugning the integrity of the government, ‘[t]he Government’s response was invit-ed_’” United States v. Swiatek, 819 F.2d 721, 731 (7th Cir.1987) (quoting United States v. West, 670 F.2d 675, 689 (7th Cir.), cert. denied sub nom. King v. United States, 457 U.S. 1124, 102 S.Ct. 2944, 73 L.Ed.2d 1340 (1982)). Although “[t]he doctrine of invited response is not a safety zone within which prosecutors may seek' refuge[,]” United States v. Torres, 809 F.2d 429, 447 (7th Cir.1987) (Flaum, J. concurring), in this case the defendant plainly provoked the prosecutor into responding to the attack on Schwe-de’s credibility. Of course, “the fact that a prosecutor’s comments may have been provoked by the defense is at best only an excuse — not a justificationf.]” Smatek, 819 F.2d at 731.
We next observe that the district court properly instructed the jury as to Schwede’s testimony. The court reminded the jury that Schwede had received benefits from the government for participating in the *1402investigation and the trial, and it advised the jurors of the possibility that Schwede’s testimony may have been influenced by the benefits she received and that the jurors could take this fact into consideration when evaluating her testimony. Not only did the court’s instructions advise the jurors that they were to consider only the evidence received in the case, and that the prosecutor’s remarks made in closing argument were not evidence, but furthermore the instructions specifically advised the jurors that they were the sole judge of the credibility of the witnesses.
These instructions effectively addressed the risk the vouching presented and sufficiently dispelled any prejudicial effect the vouching may have had. “We rely on our belief that juries heed the instructions.” United States v. Severson, 3 F.3d 1005, 1015 (7th Cir.1993). Similar instructions have repeatedly been found to dispel the risk and/or harm of vouching: see id. (district court instructed the jury “that it was the jury, not the prosecutor, who decided the credibility of witnesses”); Henry, 2 F.3d at 795 (district court “properly instructed jury that counsel’s closing arguments were not to be considered evidence”); United States v. Keskey, 863 F.2d 474, 480 (7th Cir.1988) (court instructed jury “to consider [witness’s] testimony with caution and great care”); United States v. Mealy, 851 F.2d 890, 900 (7th Cir.1988) (“[t]he judge specifically instructed the jury that they should consider the testimony of the government witness with caution and great care_ The instruction was sufficient to dispel any possible inference that the government could vouch for the witness”).
Because the jury acquitted Davis on the illegal transfer of a firearm charge, one might reasonably argue that the jury did in fact have some question as to the credibility of Schwede’s testimony concerning that specific crime. Thus, Davis’s claim that hé was harmed by prosecutor’s remarks is without merit.
On balance, after reviewing the comment in context and after considering the transcript (258 pages) of this two-day trial, we conclude that the remark does not warrant reversal. Initially, Schwede’s truthfulness was irrelevant to the two possession convictions, both of which were convincingly established by evidence wholly independent of Schwede. Davis’s own testimony and stipulations established his guilt beyond a reasonable doubt under 18 U.S.C. § 922(g)(1) (felon in possession of a firearm). Under 26 U.S.C. § 5861(d) (possession of a non-registered firearm), the only disputed issue concerned when the barrel was shortened; on that issue, based on the wear and rust at the point where the barrel had been cut, the jury concluded the barrel had been shortened long before Davis sold the sawed-off shotgun to Schwede. Second, the prosecutor’s remarks, although perhaps somewhat zealous, were invited and were made only in response to Davis’s attack on Schwede’s character; moreover, his comments were limited to rebutting Davis’s attack. Third, the district court’s instruction to the jury that it should consider Schwede’s credibility in light of the evidence presented at trial and the benefits she received for assisting in the investigation and for testifying was proper. Furthermore, the court was also careful to caution the jurors that the prosecutor’s arguments were not evidence. Finally, although we obviously do not know with certainty what degree of weight the jury gave Schwede’s testimony, the jury’s acquittal on the only charge in which Sehwede’s credibility was pertinent suggests the jury was not swayed by the prosecutor’s remarks. In sum, we agree with the district court’s observation that Davis was not prejudiced by the prosecutor’s invited response. We hold the district court did not abuse its discretion by denying Davis’s motion for a mistrial based on Davis’s allegation of improper vouching.
B.
Davis also contends he was unduly prejudiced by other remarks made by the government in rebuttal. Specifically, he points to the prosecution’s references to his case as “hogwash,” “trash,” and “garbage,” to the shotgun as “death,” and to arguably inflammatory remarks about hand grenades. We agree that the prosecutor’s remarks may have been undignified and ill-chosen for a professional who is bound by the rules of *1403civility and proper court decorum, but after considering the likely impact of the remarks in their totality, we are unconvinced the comments “so infected the trial with unfairness as to make the resulting conviction a denial of due process.” Darden v. Wainwright, 477 U.S. 168, 181, 106 S.Ct. 2464, 2471, 91 L.Ed.2d 144 (1986). The comments, whether considered separately or cumulatively, did not deprive Davis .of a fair trial.
III. Outside Influence on the Jurors
Davis contends that certain acts and omissions by the district court concerning the jury’s deliberations entitle him to reversal. He argues the court erroneously replaced one juror with an alternate after deliberations had begun, contrary to the Federal Rules of Criminal Procedure (specifically, Rules 23(b)1 and 24(c),2 as discussed infra). Observing that the trial judge neglected to caution the jurors to refrain from discussing the case, Davis maintains the court compounded the harmful effect of the omission by failing to ascertain, prior to seating the replacement juror, whether the replacement juror had, in fact, discussed the case. He also contends the court erred when refusing to replace a third juror. The relevant facts follow.
A.
The judge read his final instructions to the jury late in the afternoon on Monday, July 8th, 1992. In addition to the instructions, cited previously, that the jurors were “to consider only the evidence received in the ease,” the court instructed the jury that “[ajnything you may have seen or heard about this case outside the courtroom is not evidence and must be entirely disregarded.” No one, Davis’s counsel included, noticed that the court neglected to recite the usual admonition that the jurors should not discuss the case with anyone at all except among themselves until they had heard all the evidence and the court had given them the instructions regarding the law to be applied to the facts of the ease. After finishing the reading of the instructions, the judge excused the alternate jurors, Mr. Dunbar and Mr. Dobda. As the 12 jurors prepared to enter the jury room for deliberations, the judge remarked to the panel that he would “leave it up to you as to how late you deliberate this evening,” and that it was all right if they deliberated for an hour or so, but that “my recommendation would be that you come back and start again tomorrow morning[.]” With the additional instruction that “[w]hen you retire to the jury room, you should select one of your number as foreperson to preside over your deliberations!;,]” the jury retired to the jury room at precisely 4:30.
Shortly thereafter, within two or three minutes, the court realized it had failed to explain the three verdict forms to the jury and ordered that the jury return to the courtroom for the necessary explanations. The court finished instructing the jury about 4:36 p.m. At 4:43, just eight minutes later, the judge reported to counsel that “the first thing they [the jurors] did when they went back to the jury room was to tell the marshal that they want to go home and come back tomorrow morning to commence their deliberation then.” The judge promptly dismissed the jurors for the day.
As the jury left the courtroom, the Assistant United States Attorney observed that one of the jurors left in the company of a woman who had been present throughout the trial. He reported this to the court. After the court determined that the woman in question was the wife of Juror Castillo, the court instructed the clerk to telephone first alternate juror Dunbar (just excused), and order him to return to the court the next morning.
Early the next morning, the court met with the attorneys to discuss if there was any reason why Juror Castillo should be disquali-*1404fled from sitting as a juror on the case. Counsel for Davis stated “the defense has no objection to replacing Mr. Castillo.” The district court then called Juror Castillo into chambers and questioned him regarding the woman with whom he was seen conversing. Juror Castillo confirmed that the woman referred to was his wife and explained that she was in the courtroom because she had suffered a heart attack two years previously and he had been advised not to leave her at home alone. Castillo then explained that because his wife occasionally acted as an interpreter (Spanish) in court, he and his wife, both having had experience with court proceedings, were well aware of the fact that they were not supposed to discuss pending cases. When asked if he had discussed any aspect of the ease with his wife, Juror Castillo answered that he had not, except that his wife had asked him if another particular woman in attendance was the defendant’s wife.
After Juror Castillo left, the court, the prosecutor, and counsel for Davis discussed whether to keep the juror on the panel. The prosecutor found Juror Castillo’s testimony “suspect”:
someone who is so knowledgeable about the law, who is your spouse, without any admonishment from the Court, would have absolutely no discussion and the lone discussion would be, was that his wife in the front row ... I think he is reluctant to be completely truthful with you about what happened[.]
Counsel for Davis, on the other hand, was impressed with Juror Castillo and said so:
Your Honor, my opinion was that he was credible and that I thought he really thought it through and thought, “Well, did I talk about anything with her, and, yes, there was this one thing. We talked about, you know, who was his wife,” and he just appeared credible to me, and I have no problem with him remaining on the jury-
I would withdraw my lack of [sic] objection to removing him. I think he should remain on the jury.
After considering these two viewpoints, the judge decided to keep Juror Castillo on the jury panel. As he explained,
Now, I realize the easy thing to do would be to excuse the juror and substitute the alternate, but I don’t want to disturb the regularity of the procedure unless it is necessary to do so, and it does not seem to me in this instance that it is necessary to do so. So we will go with the original 12.
It then occurred to the court, that if Davis was convicted, Davis could conceivably raise an ineffective assistance of counsel claim alleging that counsel should not have agreed to keeping Juror Castillo. Based on this concern, the judge, observing that he had “seen [such ineffective assistance claims] happen again and again,” changed his mind and announced that he was removing Castillo from the jury and replacing him with the first alternate juror, Dunbar. Davis’s attorney, who was satisfied with Castillo’s testimony and declared his desire to have the juror remain on the jury panel, was dismayed with the court’s decision and objected on the record to Castillo’s removal. After informing Juror Castillo that he had been removed, the court seated Dunbar on the jury without questioning him as to whether he had discussed the case with anyone or been influenced in any manner after leaving the courtroom.3 The court then instructed the jury (including Dunbar) to begin its deliberations.
In an unusual turn of events, Juror Castillo, after being replaced, approached counsel for Davis and disclosed that like his wife, Juror Jachim’s husband had also been in attendance during the trial. Counsel related this fact to the trial judge who interrupted the jury’s deliberations (which, by that point, had been underway for about fifteen or twenty minutes) to question Juror Jachim. When questioned, Juror Jachim initially stated she and her husband did not discuss the trial’s events, but when pressed, modified her answer and stated that there had been discussions very general in nature. After hearing Juror Jachim’s explanation, the judge remarked,
*1405while I think she was far more nervous about this than Mr. Castillo gave any evidence of being, that is an ambiguous sign and I don’t know what can be concluded about it. Probably if Mr. Dobda were immediately available, I would, for the same reason I excused Mr. Castillo, excuse [Juror Jachim] just to remove any possible question.
The judge instructed his court clerk to call Second Alternate Juror Dobda. Dobda answered the phone and responded that it would take him two hours to reach the courthouse. The judge, pressed because of his travel schedule (out-of-state judicial conference) and the delay already occasioned, concluded that keeping the jury from deliberating for two more hours while awaiting Dob-da’s arrival was inappropriate under the circumstances. After rejecting the option of waiting two hours for Dobda to arrive, the court gave Davis the choice of keeping Juror Jachim or going with an 11-member jury instead. It is interesting to note that the defendant accepted neither of the choices offered; instead, Davis wanted to continue the delay and wait for Second Alternate Dob-da to arrive. Of the two choices offered, Davis expressed his preference to keep Juror Jachim rather than proceed with an 11-per-son jury, but he still objected to Juror Ja-ehim “on the grounds that she has had communication with her husband, who was present in the courtroom for matters excluding the jury.”
After hearing Juror Jachim’s account and observing her demeanor, the district court disagreed with Davis’s attorney’s assessment of the juror, finding that “there is no reason to believe that Mrs. Jachim has been influenced or contaminated by her discussions with her husband and that it is unreasonable to delay jury deliberations or to interrupt jury deliberations awaiting the arrival of Mr. Dobda.” Acting in accordance with Davis’s stated preference, the court allowed Juror Jachim to remain on the jury and instructed Jachim and the rest of the jurors to resume their deliberation. The jurors returned their guilty verdicts approximately five hours later.
Some seven days after the jury had completed its services in the trial, Davis submitted a post-trial motion to the court which, among other things, requested, without any supporting factual information, that the court “determine the extent the outside influences affected the deliberations^]” A single sentence in the motion offhandedly mentioned, without any facts or further elaboration, much less legal argument, that “[t]he Court also erred in not granting Davis’s motion for mistrial based on the jury improprieties.” The motion was denied.
B.
Davis contends that “the district court committed prejudicial error and violated [the Federal Rules of Criminal Procedure] by substituting, over [his] objection, Juror Castillo with an alternate after the jury had begun its deliberation, thereby denying [him] his right to a fair trial.” He merely speculates that because the court neither advised Alternate Juror Dunbar to refrain from discussing the ease with anyone nor questioned Dunbar about whether he had, in fact, discussed the case, there is no way to be sure Dunbar deliberated impartially.
Davis, however, failed to preserve for appellate review the issues he now raises. Although counsel may have objected to the removal of Juror Castillo, the transcript eloquently demonstrates that counsel did not object to the use of Alternate Juror Dunbar as Castillo’s replacement. When discussing whether to keep Castillo on the jury panel, counsel for Davis said,
Your Honor, my opinion was that he was credible and that I thought he really thought it through and thought, “Well, did I talk about anything with her, and, yes, there was this one thing. We talked about, you know, who was his wife,” and he just appeared credible to me, and I have no problem with him remaining on the jury.
I would withdraw my lack of [sic] objection to removing him. I think he should remain on the jury.
When the court decided to remove Juror Castillo to ward off a possible ineffective *1406assistance of counsel claim and replace Castillo with the alternate, counsel objected without elaboration because he was impressed with Castillo’s demeanor and wanted him to remain on the jury. Following the court’s decision, all discussion about juror replacement ceased at this point. Not only did defense counsel fail to raise any of the concerns pertaining to Dunbar that he now raises, but counsel never even mentioned Dunbar’s name. Earlier in that same proceeding, when a question as to Juror Castillo’s possible exposure to outside influence arose, defense counsel requested that the court ask Castillo “if he has had any discussions with other jurors.” The court promptly responded:
That is a good point, and I shall do that. When I call him in and I inquire of him, I will ask him questions, and then if any of you have any questions you want me to ask or ask yourself, go ahead. You may want me to ask them so that you would avoid offending him if he should be retained.
Based on the court’s willingness to immediately accommodate counsels’ questioning of Castillo, we have no doubt that had defense counsel timely requested the court to interrogate Dunbar concerning any possible outside influence the court would have done so.
On appeal, counsel argues that because there were deliberations the previous day (even though the record reflects to the contrary), it was inappropriate to use an alternate under Rules 23(b) and 24(c); but according to the record, when the substitution was made, counsel did not assert that there had been deliberations on Monday; indeed, he did not mention Rules 23(b) or 24(c), much less raise an objection based on those rules. Counsel now argues that the court’s failure to caution Dunbar to refrain from discussing the case may have been prejudicial; but counsel made no objection of this nature when the court neglected to give this instruction on Monday afternoon. Counsel again failed to raise an objection on this ground the next morning, when Dunbar was substituted for Castillo. Counsel also now argues, again for the first time, that the court failed to question Dunbar about disqualification due to the possibility of outside influence. In short, counsel failed to alert the court to any of the concerns he now raises about the propriety of Dunbar’s service on the jury, and thus failed to give the district court an opportunity to rule on, much less rectify, any of the alleged errors. After registering his objection to the court’s decision to remove Juror Castillo, Davis simply acquiesced, without objection, to the court’s judgment to use Alternate Juror Dunbar as Castillo’s replacement.
Not until one week after the verdicts had been rendered and the jury discharged did Davis, in a post-trial motion, initially raise the speculative question of whether the jury may have been illegally constituted or improperly seated; even at that time, however, Davis failed to make any objection, much less a specific one, or set forth any of the facts, much less arguments, upon which he now relies. We must point out that once again Davis made no reference to 1) Dunbar, 2) Rules 23(b) or 24(c), 3) the fact that the court neglected to caution the jurors to refrain from discussing the case, or 4) the court’s failure to question Dunbar about the possibility of outside influence before seating him on the jury panel. Having never breathed a word — until now — about the issue of the appropriateness of Dunbar’s substitution, we refuse to countenance Davis’s argument that he has preserved the right to raise these issues on appeal.
As our Supreme Court recently stated, “ ‘[n]o procedural principle is more familiar to this Court than that a constitutional right,’ or a right of any other sort, ‘may be forfeited in criminal as well as civil cases by the failure to make timely assertion of the right before a tribunal having jurisdiction to determine it’.” United States v. Olano, - U.S. -, -, 113 S.Ct. 1770, 1776, 123 L.Ed.2d 508 (1993) (quoting Yakus v. United States, 321 U.S. 414, 444, 64 S.Ct. 660, 677, 88 L.Ed. 834 (1944)). “To preserve an issue for appellate review, a party must make a proper objection at trial that alerts the court and opposing party to the specific grounds for the objection.” United States v. Wynn, 845 F.2d 1439, 1442 (7th Cir.1988). A timely and proper objection apprises the court of the precise nature of the alleged *1407error so the court has an opportunity to rectify any shortcoming, United States v. Lewis, 954 F.2d 1386, 1391 (7th Cir.1992), but vague, unspecific objections preserve nothing, except perhaps a lingering monument to their inadequacy. “Neither a general objection to the evidence nor a specific objection on other grounds will preserve the issue for review,” Wynn, 845 F.2d at 1442, and “the specific ground for reversal of an evidentiary ruling on appeal must also be the same as that raised at trial.” Id. The defendant may not present an argument on appeal different from that presented at trial because the trial court had no opportunity to address, much less rectify, the alleged problem asserted for the first time on appeal. See United States v. Blackwood, 768 F.2d 131, 136 (7th Cir.), cert. denied, 474 U.S. 1020, 106 S.Ct. 569, 88 L.Ed.2d 554 (1985).
By failing to object to the use of Dunbar as a replacement for Castillo, Davis has forfeited4 his right to predicate an appeal on the district court’s substitution. His only recourse lies in Fed.R.Crim.Pro. 52(b), which states that “[pjlain errors or defects affecting substantial rights may be noticed although they were not brought to the attention of the court.”
In Olano, our Supreme Court recently “granted certiorari to clarify the standard for ‘plain error’ review by the Courts of Appeals under Rule 52(b).” Olano, — U.S. at -, 113 S.Ct. at 1776. There, the district court, without objection from the defendants, allowed two alternates to sit in on the jury’s deliberations with the instruction that the alternates were not to participate in the deliberations in any way.5 During deliberations, one alternate juror was excused at his request, but the other remained in the jury room until the jury returned its verdict. Because the defendants had not objected to the alternates’ presence in the jury room during deliberations, the Ninth Circuit applied a plain error standard under Rule 52(b) and reversed the convictions after holding the presence of the alternates violated Rule 24(c) and was inherently prejudicial. The Supreme Court reversed, concluding that because alternates’ presence did not affect the defendants’ substantial rights, the Court of Appeals had no authority to correct the error. Olano, — U.S. at -, 113 S.Ct. at 1781.
As the Supreme Court explained, application of Rule 52(b) is “circumscribed” to only those 1) “errors” that are 2) “plain” and that 3) “affect substantial rights.” Id. at 1776. In other words, the Court of Appeals may not correct (either by vacating for a new trial or reversing outright) errors which, at a minimum, do not meet all three criteria. Id. at -, 113 S.Ct. at 1777. But even if the forfeited error does meet all three criteria, reversal is still not necessarily required; the decision to correct a plain error affecting a defendant’s substantial rights lies “within the sound discretion of the Court of Appeals[.]” The Court of Appeals, however, “should not exercise that discretion unless the error ‘seriously affect[s] the fairness, integrity or public reputation of judicial proceedings.’ ” Id. at -, 113 S.Ct. at 1776 (citation omitted). Thus, a defendant who has failed to make a timely assertion of a right must meet four requirements in all before he can receive relief under Rule 52(b): that there was error, that the error was plain, that the plain error affected his substantial rights, and that the plain error which affected his substantial rights also seriously affected the fairness, integrity, or public reputation of judicial proceedings. Id. at -, 113 S.Ct. at 1779.
The “error” contemplated by Olano is “deviation from a legal rule,” unless the rule has been waived. Id. at -, 113 S.Ct. at 1777. “If a legal rule was violated during the District Court proceedings, and if the defendant did not waive the rule, then there has been an ‘error’ within the meaning of Rule 52(b) despite the absence -of a timely objection.” Id. “‘Plain’ is synonymous with ‘clear’ or, *1408equivalently, ‘obvious’[,]” and “[a]t a minimum, the Court of Appeals cannot correct an error pursuant to Rule 52(b) unless the error is clear under current law.” Id. “Affecting substantial rights” normally means that “the error must have been prejudicial,” i.e., “must have affected the outcome of the District Court proceedings.” Id. at -, 113 S.Ct. at 1778 (our emphasis). Significantly, under Rule 52(b) “[i]t is the defendant rather than the Government who bears the burden of persuasion with respect to prejudice.” Id. (our emphasis). Because the defendants in Olano did not demonstrate that the alternates’ presence in the jury room during the jury’s deliberations was prejudicial, the Court of Appeals had no authority to correct the error. Id. at -, 113 S.Ct. at 1781.
Keeping Olano’s principles in mind, we turn to Davis’s case.
Davis claims the court’s substitution of Alternate Juror Dunbar for Juror Castillo deviated from Rules 23(b) and 24(c) of the Federal Rules of Criminal Procedure. He notes that under Rule 23(b), “if the court finds it necessary to excuse a juror for just cause after the jury has retired to consider its verdict, in the discretion of the court a valid verdict may be returned by the remaining 11 jurors.” Under Rule 24(e), “alternate jurors in the order in which they are called shall replace jurors who, prior to the time the jury retires to consider its verdict, become or are found to be unable or disqualified to perform their duties.” Davis observes that the Fifth Circuit has read Rules 23(b) and 24(c) together to mean that after a jury has begun deliberations, it is error to substitute an alternate rather than proceed to verdict with an 11-member jury; when a juror becomes unable to continue deliberations, the only two proper courses are mistrial or an 11-member jury. United States v. Huntress, 956 F.2d 1309, 1314-17 (5th Cir.1992), cert. denied, — U.S. -, 113 S.Ct. 2330, 124 L.Ed.2d 243 (1993). Likewise, Davis notes that this court has stated that the rules do not provide for recalling an alternate after he is discharged and that policy as well as the language of Rule 24(e) forbid the practice. United States v. Josefik, 753 F.2d 585, 587 (7th Cir.1985), cert. denied, 471 U.S. 1055, 105 S.Ct. 2117, 85 L.Ed.2d 481 (1985). The concern underlying the rules is that •
[a]n alternate who joins the jury’s deliberations after they have begun, even if he has not discussed the case with other people or forgotten the judge’s (other) instructions in the interim, will be at a disadvantage in holding his own with the other jurors, and as a result, the defendant may not really be getting the jury of 12 to which he is entitled.
Id.
In Josefik, a. juror asked to be excused nine minutes after deliberations had begun. With the defendant’s consent, the juror was replaced with an alternate. This court noted that Rule 24(c) contains no provision for recalling an alternate after he or she has been discharged, but that doing so does not automatically amount to reversible error, since “only prejudicial violations of the rules are reversible errors.” Id. (citations omitted) (emphasis added). Because only nine minutes of deliberations had occurred when the alternate joined the jury, the alternate juror “didn’t miss anything important and could deliberate on par with the original jurors.” Id. Further, by consenting to the procedure, the defendant waived the right to challenge it on appeal. Id. at 588.6
Contrary to the heart of Davis’s argument, the factual situation in this case does not implicate the concern underlying Rules 23(b), 24(c), and Josefik because in this case, *1409as contrasted with the facts of Josefik, although the jury had retired, it had not as yet begun to consider its verdict when the district court decided to replace Juror Castillo with Alternate Dunbar. After giving final instructions to the jury, the court specifically recommended “that you come back and start again tomorrow morning[.]” Obviously, the jurors followed this advice: as the court reported to the attorneys, “the first thing they did when they went back to the jury room [at 4:35 p.m.] was to tell the marshal that they want to go home and come back tomorrow morning to commence their deliberation then.” Not only were there no deliberations after 4:35 p.m., but there were no deliberations before 4:35 p.m., considering that it is customary for jurors to first introduce themselves to each other and elect a jury foreperson before actually considering the merits of the evidence presented to them during the trial. . The court instructed the jury that “[w]hen you retire to the jury room, you should select one of your number as foreperson to preside over your deliberations.” Also between 4:30 p.m. and 4:35 p.m., the court realized it had neglected to explain the verdict forms, called the jury back to the courtroom, explained the forms, and sent the jury back to the jury room.
Thus, when Dunbar joined the jury Tuesday morning he had missed no deliberations and was therefore able to deliberate on a par with each of the other jurors as. to each and every element of the crimes charged. Accordingly, Davis’s argument that the court erroneously replaced one juror with an alternate after deliberations had begun is inaccurate, because there had been no deliberations when the substitution was made. Since the jury had not commenced deliberating, the concern in Josefik simply is not involved in this case. We note that when Davis later rejected the court’s offer of proceeding with an 11-member jury after the issue of Juror Jachim’s possible taint arose 15 to 20 minutes into the jury’s deliberations, there is no reason to believe Davis would have accepted an 11-member jury, had it been offered, when the issue of Juror Castillo’s possible disqualification arose. (Of course,, because the jury had not begun to consider its verdict when the district court seated Dunbar on the jury panel, there was no need for the court at that time to offer Davis the option of an 11-member jury.)
Even if we were to assume for the sake of argument that there might have been a minuscule amount of deliberation on Monday afternoon, reversal would still not be warranted. Assuming that “error” (that is, “deviation from a legal rule”) occurred in the substitution procedure, and that the error was “plain,” assumptions with which we do not agree but will consider as true only for the purposes of discussion, we still are at a loss to understand how Davis can argue, much less conclude, that he has met his burden under Olano of demonstrating that the error affected his substantial rights by having an effect on the outcome of the district court proceedings. The evidence of Davis’s guilt on Count I, possession of a firearm by a felon, was proven by Davis’s own testimony and stipulations; it is difficult to understand how a defendant who admits to facts establishing his guilt can be prejudiced by the participation of a replacement juror. It is also difficult to understand how Dunbar’s presence on the jury could have had an effect on Davis’s conviction under Count II, possession of a non-registered firearm, given the physical evidence and the expert testimony that the point where the barrel was cut had accumulated four to five years’ worth of rust. It is inconceivable that the court’s placement of Dunbar on the jury prejudiced Davis.
Under Olano’s plain error- analysis, this court has no authority to grant a defendant relief until the defendant (and not the government) has shown the existence of a “plain” “error” that “affected the defendant’s substantial rights.” Only when a defendant meets all three of these requirements will we then consider whether the defendant has demonstrated that the plain error affecting his substantial rights also “seriously affect[s] the fairness, integrity, or public reputation of judicial proceedings.” Olano, — U.S. at -, 113 S.Ct. at 1776. We hold Davis has failed to establish that Alternate Juror’s presence on the jury panel was plain error and that Dunbar’s presence affected his substantial rights by affecting the outcome of *1410the proceedings. Accordingly, there is no need to consider the fourth component of the plain error analysis. This court has no authority to grant Davis relief.
C.
Davis raised no objection to Dunbar’s substitution either during trial or in the post-trial motion. He never requested the district court question Dunbar about the nature of any conversations Dunbar might possibly have had during the 16-hour period between his release on Monday afternoon and his return to court on Tuesday morning. He has utterly failed to demonstrate how the district court’s decision to replace Castillo (who, we note, was Davis’s choice to sit on the jury) with Dunbar in any way adversely affected the jury’s two guilty verdicts. The record contains not one scintilla of evidence to establish that Dunbar should have been disqualified to sit as a juror. Our research of the case law, as discussed shortly, has revealed no convictions being overturned based solely on self-serving speculation, wholly unsupported, that a defendant “faced a significant possibility of jury taint,” as the dissent has phrased the issue. Notwithstanding each and every one of these facts, the dissent insists Davis’s convictions should be reversed, arguing “the majority simply does not have an adequate record upon which to base its conclusion that Davis was not prejudiced.” This argument misses the mark.
First, the dissent’s proposition that the record is inadequate to show Davis was not prejudiced cleverly but mistakenly shifts the burden of persuasion of disproving prejudice from the defendant to the government. Under Rule 52(b), the burden of proving the existence of prejudice (that is, an effect on the proceedings) lies with the defendant, not the government: “Rule 52(b) normally requires the same kind of inquiry [as Rule 52(a)], with one important difference: It is the defendant rather than the Govern- - ment who bears the burden of persuasion with respect to prejudice.” Olano, — U.S. at-, 113 S.Ct. at 1778. Davis failed to meet his burden of demonstrating that Dunbar’s presence on the jury affected the proceedings. We refuse to assume a defendant has been prejudiced in the absence of any proof or documentation to the contrary. In any event,- we have already demonstrated that Davis’s argument falls far short under the Olano plain error analysis, even when we assumed- for the sake of argument only that there had been plain error.
Second, there is no reason whatsoever to believe Dunbar was biased or even might have been; the conclusion that Dunbar may have been improperly influenced is mere self-serving speculation. In fact, the record is more than adequate to conclude that Dunbar was not influenced.
After having heard all the evidence with the entire jury panel, and after specifically being instructed that “[a]nything you may have seen or heard about this case outside the courtroom is not evidence and must be entirely disregarded,” Dunbar was discharged on Monday afternoon. Shortly after his discharge, the court clerk called Dunbar and directed him to return to court the following morning. Having just been ordered to return to court the next morning, and having previously been admonished in the court’s jury instructions that anything said or heard about the base outside the courtroom must be entirely disregarded, Dunbar most assuredly would have been alerted to the fact that he should not discuss the case. While it is true the district court did not instruct Dunbar to refrain from discussing the case, it plainly sent the same message when it instructed Dunbar that anything said or heard outside the courtroom was not evidence and must be disregarded. We rely upon a belief that jurors heed the instructions they have been given, Severson, 3 F.3d at 1015, and we note that Dunbar, like every other juror, was examined, cross-examined, found to be impartial and acceptable to Davis during voir dire examination, and took the oath to act faithfully as a juror if called upon.
Moreover, it is reasonable to assume that during the period Dunbar was away from the court, it took him quite a period of time to travel to and from the courtroom and his home (in heavy Chicago rush hour traffic), eat dinner, prepare for bed, sleep, awake, wash, dress, and eat *1411breakfast. The record demonstrates Dunbar had little time to do anything other than the listed activities. While Davis speculates that Dunbar “almost certainly did” discuss the ease when he went home Monday evening, there is no evidence in the record that Dunbar even lives with anyone, let alone that he discussed the case, and still less that he became influenced thereby. As the district court itself noted when discussing the possibility of Juror Castillo’s disqualification, Davis’s ease was not publicized; the court remarked that “obviously this is not a case of any notoriety.” And as we observed above, the fact that the clerk called Dunbar and told him he was needed in court the next morning undoubtedly reminded Dunbar that he should not let any outside sources influence him. There simply is nothing in this record to give credence to the defendant’s self-serving assumption that Dunbar was subjected to influence by outside sources and that he did not heed the district court’s admonition to disregard anything seen or heard about the case outside the courtroom. There is certainly nothing wrong with or prejudicial about a juror individually pondering the evidence he or she has heard after the testimony has been completed and while away from the courtroom. Neither is there anything objectionable about a juror’s assimilating and analyzing all of the evidence received in an attempt to begin to form an opinion, so long as that opinion is one’s own and is based solely upon all of the evidence presented at trial.
There is yet another reason to believe Dunbar was impartial and did, in fact, cast his vote based solely on the testimony and evidence: the fact that Dunbar joined his fellow jurors and voted to acquit Davis on the illegal transfer charge, the only charge that was reasonably disputed. If Dunbar was prejudicially influenced by anything he saw or heard during the 16 hours he was away from court, why did he vote to acquit? Even the fact that Dunbar voted to convict Davis on the two possession counts shows his impartiality, given the degree of rust at the point where the barrel was shortened and Davis’s own admissions, stipulations, and testimony. Whether Davis likes it or not, the evidence relating to the two possession charges was airtight.
As if all this were not enough to establish Dunbar’s impartiality, there is still more! Midway through deliberations the jury submitted a question to the court. The court called the respective attorneys and the defendant together and read the note:
The Court: It is 11:35 a.m. The jury has handed a note to the marshal which reads as follows:
“Your honor, we, as the jury, would like to know: When a person takes possession of a weapon manufactured without a serial number, what is the required registration process by law?”
And this is signed by A.W. Dunbar. [Counsel for Davis]: Interesting question. It sounds like they were paying attention.
Counsel was right — the jurors were paying attention, and it appears Alternate Juror Dunbar was leading the way, judging from the fact he alone signed the note. Far from suggesting partiality and bias, the record strongly suggests that Dunbar was neither partial nor biased.
Although it would have been preferable for the court to have questioned Dunbar as to any possible outside influences at the time Dunbar replaced Castillo on the jury, no such timely request was made by defense counsel. Even in the absence of a motion by defense counsel to question a juror, we must make it clear that it is advisable for a trial judge to interrogate on the record any juror being recalled to serve on a jury who had previously been excused in order to ascertain whether he may conceivably have been exposed to an outside influence. When the defendant finally did move to examine the jurors for possible outside influences seven days after completion of the trial, had the judge conducted a brief interrogation of juror Dunbar concerning whether he had been exposed to outside influences, in all probability this issue would not be before us.7 Nonethe*1412less, we hasten to point out that we disagree with the dissent’s allegation that “Davis faced a significant possibility of jury taint” for that assertion is based on nothing but mere speculation.
D.
Notwithstanding the compelling evidence contradicting the dissent’s position that there was a significant possibility Dunbar was tainted, the dissent contends reversal is warranted simply because the court failed to advise Dunbar to refrain from discussing the case and failed to question him about whether he did, in fact, discuss the ease.
It is true that a criminal defendant has the right to be tried by a jury whose verdict is based solely on the evidence received by the jury in open court. Sheppard v. Maxwell, 384 U.S. 333, 86 S.Ct. 1507, 16 L.Ed.2d 600 (1966). If there is a “reasonable possibility” that a jury’s verdict has been affected by material not properly admitted as evidence, the criminal defendant is entitled to a new trial. United States v. Andrews, 895 F.2d 406, 408 (7th Cir.1990) (citing United States v. Bruscino, 687 F.2d 938, 940 (7th Cir.1982) (en banc)). “The ultimate inquiry is whether there is any substantial likelihood that the defendants were denied a fair trial.” United States v. Balistrieri, 779 F.2d 1191, 1214 (7th Cir.1985). Moreover, “the law does not require that a defendant receive a perfect trial, only a fair one_” Michigan v. Tucker, 417 U.S. 433, 446, 94 S.Ct. 2357, 2365, 41 L.Ed.2d 182 (1974).
Once a defendant has made a sufficient showing that a juror may have been improperly influenced, the court must ascertain whether the juror was or was not tainted. See Remmer v. United States, 347 U.S. 227, 74 S.Ct. 450, 98 L.Ed. 654 (1954); United States v. Sanders, 962 F.2d 660, 671 (7th Cir.), cert. denied, — U.S. -, 113 S.Ct. 262, 121 L.Ed.2d 192 (1992) (district court “presented with reports of prejudicial publicity ... is required ... to inquire of the jurors about their knowledge, if any, of the reports”). Once the defendant has made a colorable showing of the possibility of taint he may invoke Federal Rule of Evidence 606(b), which permits a juror to testify after the verdict has been rendered “on the question of whether extraneous prejudicial information was improperly brought to the jury’s attention” and on “whether any outside influence was improperly brought to bear upon any juror.”
The question raised herein is far removed from the applicable fact and law referred to above, for in the case before us the defendant, without supporting information, did nothing more than speculate that his jury may have been subjected to outside influence. A court is under no obligation to inquire into the possibility of improper influence until the defendant comes forward with a colorable allegation of taint. “It is only when the defendant has made a colorable showing of extrinsic evidence that the court must investigate the asserted [jury] impropriety.” United States v. Ayarza-Garcia, 819 F.2d 1043, 1051 (11th Cir.), cert. denied, 484 U.S. 969, 108 S.Ct. 465, 98 L.Ed.2d 404 (1987); see also United States v. Watchmaker, 761 F.2d 1459, 1465 (11th Cir.1985) (“the failure to hold a hearing constitutes an abuse of discretion only where there is evidence that the jury was subjected to influences by outside sources”), cert. denied, 474 U.S. 1100, 106 S.Ct. 879, 880, 88 L.Ed.2d 917 (1986). A defendant’s mere allegations of taint or his unsubstantiated suspicions do not necessitate inquiry by the court. United States v. Easter, 981 F.2d 1549, 1553 (10th Cir.1992) (“inquiry is not warranted when only ‘thin allegations of jury misconduct’ are present”), cert. denied, — U.S.-, 113 S.Ct. 2448, 124 L.Ed.2d 665 (1993); United States v. Thornton, 746 F.2d 39, 50 (D.C.Cir.1984) {“the trial court need not conduct a voir dire on counsel’s unsubstantiated suspicion”) (emphasis added). As one court put it, “the duty to investigate arises only when the party alleging misconduct makes an adequate showing of extrinsic influence to overcome the presumption of jury impartiality. In other words, there must be something more than mere speculation.” United States v. *1413Barshov, 733 F.2d 842, 851 (11th Cir.1984) (emphasis added), cert. denied, 469 U.S. 1158, 105 S.Ct. 904, 83 L.Ed.2d 919 (1985). Finally, “[t]he more speculative or unsubstantiated the allegation of misconduct, the less the burden to investigate.” United States v. Hernandez, 921 F.2d 1569, 1577 (11th Cir.), cert. denied, — U.S. -, 111 S.Ct. 2271, 114 L.Ed.2d 722 (1991). We disagree with the dissent’s proclamation that “it is absolutely essential that the recalled alternate be questioned to insure the alternate’s freedom from outside influences before reinstatement!;,]” because the eases just cited stand for the proposition that there is no requirement that a replacement juror be questioned until the defendant puts forth a sufficient reason to warrant questioning.
In this case, when the court decided to replace Juror Castillo with Alternate Juror Dunbar, Davis said nothing about Dunbar and presented the court with no reason to believe that Dunbar may have been tainted; accordingly, the court was under no obligation to conduct a hearing to ascertain whether Dunbar had been improperly influenced. Neither did the court erroneously deny Davis’s post-trial motion, which once again failed to raise any colorable showing of improper influence. Not only did Davis’s post-trial motion fail to give the court a reason to believe Dunbar was improperly influenced, it failed to even mention Dunbar’s name! Post-verdict expeditions in search of information with which to impeach the jury’s verdict (which is exactly what Davis’s post-trial motion amounted to) are improper. See United States v. Davila, 704 F.2d 749, 754 (5th Cir.1983). Because neither the court, the prosecution, nor Davis had any reason to suspect Dunbar was, in fact, tainted, and without any concern voiced by the affected party, Davis, at the time the substitution was made, the court’s failure to question Dunbar at the time of substitution was understandable. It was consistent with the common sense notion that until there is reason to suspect a juror has been tainted, inquiry is neither invited nor required.
Since there is no evidence in the record that Dunbar was, in fact, improperly influenced during the 16-hour period, and the dissent points to none, it is simply the risk that Dunbar may have been subjected to the alleged possible improper influence that the dissent finds so egregious. But the risk that a juror will be subject to outside forces is a fact of life; the only way to eliminate this supposed risk is to sequester all jurors each and every evening until they reach their verdicts! If this becomes the law then every jury panel not sequestered must be questioned each morning before deliberations resume, even if the jurors had been instructed before leaving the previous day that they were not to accept anything but the evidence they had heard during that trial in that courtroom, because there is no other way to be sure the jurors had not become tainted during the time they were out of the confines of the jury room. Of course, such a policy obviously would be both very time consuming and unnecessary, especially in a world of ever-increasing court costs to the litigants and government and the ever-increasing scarcity of judicial resources caused by the litigation explosion; we are searching for truth, not for alleged errors. As our Supreme Court stated in Olano,
[D]ue process does not require a new trial every time a juror has been placed in a potentially compromising situation. Were that the rule, few trials would be constitutionally acceptable.... [I]t is virtually impossible to shield jurors from every contact or influence that might theoretically affect their vote. Due process means a jury capable and willing to decide the case solely on the evidence before it, and a trial judge ever watchful to prevent prejudicial occurrences and to determine the effect of such occurrences when they happen.
Olano, — U.S. at -, 113 S.Ct. at 1780 .(emphasis added) (citing Smith v. Phillips, 455 U.S. 209, 102 S.Ct. 940, 71 L.Ed.2d 78 (1982)).
Based on the record before us, there is simply no reasonable possibility that the jury’s verdict was affected by material not admitted as evidence; neither is there a substantial likelihood that Davis was denied a fair trial. As we have explained at length, the record is replete with evidence that Dun*1414bar and his 11 fellow jurors deliberated impartially and completely in accordance with the testimony and evidence introduced at trial, as each juror was instructed. Dunbar’s impartiality, in addition to the truly overwhelming nature of the evidence of Davis’s guilt, conclusively disprove the dissent’s contention that “there is no evidence in the record to support the determination that Davis was not prejudiced.” Although we have no argument with the dissent’s position that it certainly would have been preferable for the district court to give the jurors the boilerplate (usual) instruction that they were not to discuss the case and to have questioned Dunbar about the possibility of influence before seating him, the failure to do so does not rise to the level of prejudicial error and did not interfere with Davis’s right to a fair trial. We hold that based on the facts in this record, the district court’s omissions do not necessitate the reversal of convictions of crimes for which Davis is guilty beyond a reasonable doubt.
E.
Davis next asserts the court erroneously and prejudicially refused to dismiss Juror Jaehim, who, like Juror Castillo, had a spouse present at the trial.
After learning that a second juror, Juror Jaehim, also had a spouse present throughout the trial, the judge consulted counsel for both parties and brought Juror Jaehim to chambers for questioning. The following exchange ensued:
The Court: Did your husband discuss with you anything that happened or anything that was said in the courtroom while the jury was not present?
Juror Jaehim: No to my knowledge he did not, not that I could think of.
The Court: Did you and your husband discuss the case at all?
Juror Jaehim: Not to the effect that whether the man is guilty or he isn’t. All we said was it is interesting to see how different people come in and that it could be confusing because evidently, somebody along the line just might not be telling the truth and we said it is like a three-ring circus ... he just said you have to weigh facts in a case like this because ... and that is what we said. Sometimes somebody looks like they are guilty and then when you listen to the facts, then it seems like somebody else isn’t telling the truth. This is the way we have done it, but to actually say the man is guilty or so and so is lying, no, that we did not.
The Court: Did your husband express any opinion as to the guilt or innocence of the defendant?
Juror Jaehim: No he didn’t. He just said you have to weigh facts in the case like this because — and that is what we said. Sometimes somebody looks like they are guilty and then when you listen to the facts, then it seems like somebody else isn’t telling the truth. This is about the way we have done it, but to actually say the man is guilty or so and so is lying, no, that we did not. The Court: Can you recall anything he said to you about his own observations about the case or anything that he heard about the case?
Juror Jaehim: No.
******
The Court: Do counsel have any questions they would like to ask?
[Counsel for Davis]: No, sir.
[Counsel for the government]: None, your honor. The government does not have any.
The Court: All right, thank you, Mrs. Ja-chim. You can go back to the jury room, and will you tell the other jurors that I ask that you interrupt your deliberations at this point. Don’t deliberate any further until you hear from me again. Thank you very much.
Davis somehow insists that this testimony demonstrates Juror Jaehim “discussed vital issues, including the very guilt or innocence of the defendant and the credibility of the witnesses.” By her own words, however, Juror Jaehim emphatically denied having discussed Davis’s guilt or innocence. Her testimony was given in the absence of the jury, under oath, during a special hearing in the court’s chambers with the judge and the respective attorneys present. Counsel for *1415Davis was given the opportunity to question Juror Jachim but declined. Because by this time there had been 15 or 20 minutes of deliberation, the court offered Davis the option of proceeding with an 11-member jury, pursuant to Rule 23(b), but counsel refused. Davis’s counsel refused to accept any one of the alternatives the court offered. Counsel 1) argued that the court should keep Juror Castillo, 2) insisted that the court remove Juror Jachim, and 3) objected to both of the choices the court offered him (11-member jury or keep Jachim) after it was learned that Alternate Juror Dobda was unavailable. After having had the opportunity to review and weigh her testimony as well as assess her demeanor, the court concluded Juror Ja-chim was qualified to sit as a juror. We are not here to second-guess the court’s factual determinations.
Even if we were to agree with Davis’s assessment of taint, which we do not, we refuse to conclude on the record before us that there exists a reasonable probability the verdict was affected by Juror Jachim’s contact with her husband. Why? Because even if we presume prejudice, “a presumption of prejudice as opposed to a specific analysis does not change the ultimate inquiry: Did the intrusion affect the jury’s deliberations and thereby its verdict?” Olano, — U.S. at -, 113 S.Ct. at 1780. Given the virtually unassailable evidence of Davis’s guilt, it would be impossible to conclude that Juror Jaehim’s contact with her husband affected the jury’s deliberations and verdicts.
We hold the court’s refusal to dismiss Juror Jachim was neither erroneous nor prejudicial, as Davis has claimed.
IV. Outrageous Conduct
Finally, Davis contends the government’s outrageous conduct denied him due process of law. We review this issue de novo. United States v. Valona, 834 F.2d 1334, 1343 (7th Cir.1987). ‘Whether the government has stepped beyond permissible constitutional bounds in attempting to enforce the law is a legal question, not a factual one.” Id. (citing United States v. Swiatek, 819 F.2d 721, 726 (7th Cir.1987)).
Specifically, Davis claims Schwede bought heroin for him before and after the gun sale, lent him money (presumably government money), and used drugs herself over many years. Observing Schwede was paid nearly $40,000 over the course of three years, Davis asserts the money would have been better spent in drug treatment programs rather than in inducing crime and then prosecuting it. In a further attempt to reach out, Davis notes that after returning its verdicts, the jury read a statement voicing its disapproval of certain aspects of the government’s investigation.
The outrageous government conduct doctrine presents an extremely narrow opportunity for a defendant to challenge government conduct violating his due process rights. United States v. Olson, 978 F.2d 1472, 1481 (7th Cir.1992), cert. denied, — U.S. -, 113 S.Ct. 1614, 123 L.Ed.2d 174, 175 (1993). The theory stems from dicta in United States v. Russell, 411 U.S. 423, 93 S.Ct. 1637, 36 L.Ed.2d 366 (1973), in which then Justice Rehnquist opined, “we may some day be presented with a situation in which the conduct of law enforcement agents is so outrageous -that due process principles would absolutely bar the government from invoking judicial processes to obtain a verdict.” Id. at 431-32, 93 S.Ct. at 1643. Both a plurality of the Supreme Court and this circuit have expressed doubt as to the validity of the doctrine of outrageous conduct. See Hampton v. United States, 425 U.S. 484, 490, 96 S.Ct. 1646, 1650, 48 L.Ed.2d 113 (1976); United States v. White, 950 F.2d 426, 431 (7th Cir.1991). At least one member of this circuit court has called for an outright rejection of the doctrine. See United States v. Miller, 891 F.2d 1265, 1271 (7th Cir.1989) (Easterbrook, J. concurring). We decline Davis’s invitation to invoke the doctrine in this instance.
Davis would have us adopt his version of events en toto. He ignores Schwede’s testimony, unfavorable to him, that she did not use drugs and never purchased any for Davis. The use of unsavory informants like Schwede in undercover police investigations is “an unattractive business, but that is the nature of the beast....” United States v. *1416Kaminski, 708 F.2d 1004, 1010 (7th Cir.1983). That the informants are used and are paid to provide information is not per se outrageous; in fact it is a necessity of crime fighting, as much as we might find it distasteful. The jury may consider such arrangements as evidence relating to the informant’s credibility. Olson, 978 F.2d at 1482 (citing Miller, 891 F.2d at 1268). As noted previously, the court instructed the Davis jury that in assessing credibility, it could consider the fact that Schwede was not only paid to provide information and testify, but also was not charged: “You may give [Schwede’s] testimony such weight as you feel it deserves keeping in mind whether the testimony of this witness has been influenced by the benefits she has received from the government.” As to the juror’s opinion of certain aspects of the government’s investigation, their statement is just that — an opinion, and certainly none of the aspects the jurors mentioned constitute outrageous conduct.
When a defendant raises an entrapment defense, the prosecution must prove beyond reasonable doubt that the defendant was disposed to commit the criminal act prior to being first approached by government agents. Jacobson v. United States, — U.S. -, 112 S.Ct. 1535, 118 L.Ed.2d 174 (1992). The prosecution has met its burden in this instance, since the government proved beyond a reasonable doubt that Davis possessed the weapon long before Schwede and the governmental enforcement agencies arrived on the scene. In short, we fail to understand how any action taken by the government in any manner affected the propriety of Davis’s two possession convictions. We hold Davis has faded to establish that reversal is warranted based on his outrageous government conduct allegation.
CONCLUSION
Each one of Davis’s arguments must fail. First, the evidence was sufficient for the jury to find beyond a reasonable doubt that Davis was a felon in possession of a firearm because Davis’s own testimony and stipulations established each element of that crime. Additionally, the evidence was sufficient for a jury to find beyond a reasonable doubt that Davis illegally possessed a sawed-off shotgun because based upon the evidence presented, the jury concluded that the shotgun’s barrel had accumulated four to five years’ worth of rust, thereby contradicting Davis’s claim that he was entrapped into shortening the barrel just days before the sale.
Second, although there may be some merit to Davis’s argument that the Assistant United States Attorney vouched for Debra Schwede’s truthfulness, the trial judge was in the best position to assess the effect of the allegation of vouching. We agree with the court’s assessment that the prosecutor’s remark had no prejudicial effect on Davis’s two possession convictions. Not only did the district court effectively instruct the jurors to disregard the prosecutor’s comment, but Schwede’s truthfulness was not an issue with regard to Davis’s two possession convictions, both of which were conclusively established by evidence wholly independent of Schwede and her capacity for speaking the truth. The prosecutor’s references to Davis’s ease as “hogwash,” “trash,” and the like, while undignified and ill-chosen, did not render Davis’s trial unfair.
Third, the court did not erroneously replace Juror Castillo with Alternate Juror Dunbar. The substitution was not in violation of the Federal Rules 23(b) and 24(c) of Criminal Procedure because when the replacement juror was seated, the jury had not begun to consider its verdict, and therefore the alternate was able to deliberate on a par with the original jurors. Even when we assumed solely for the sake of argument that there had been deliberations and that the rules had been violated, Davis faded to meet his burden under Olano of demonstrating that the substitution affected the outcome of the proceedings. Absent a colorable showing of the possibility of taint, the court is not required (although it is preferred) to question replacement jurors about their conduct during the time they were away from the courthouse, especially when, as was the case here, the defendant did not show the slightest concern about the alternate’s possible taint until his appeal. Neither did the court err by refusing to replace Juror Jachim; we *1417defer to the court’s factual findings concerning a juror’s impartiality because it was the district court, not us, who had the opportunity to assess the juror’s demeanor. But once again, even when we adopted Davis’s argument simply for the sake of argument, we concluded that Davis had not shown a nega-five effect on the jury’s verdicts.
Finally, the government’s conduct during its investigation of Davis was not outrageous. The use of unsavory informants is not per se outrageous and the jury was instructed that it should keep in mind the benefits Sehwede received from the government when considering the weight to give her testimony. The government met its burden of disproving beyond a reasonable doubt Davis’s entrapment defense on the two possession allegations.
For the above reasons, the judgment is AFFIRMED.
. That portion of Rule 23(b) relevant to Davis's appeal states, "if the court finds it necessary to excuse a juror for just cause after the jury has retired to consider its verdict, in the discretion of the court a valid verdict may be returned by the remaining 11 jurors."
. That portion of Rule 24(c) relevant to Davis’s appeals states that “[a]ltemate jurors in the order in which they are called shall replace jurors who, prior to the time the jury retires to consider its verdict, become or are found to be unable or disqualified to perform their duties.”
. We have no doubt whatsoever that had defense counsel requested the court to question Dunbar concerning possible outside influence, the court would have obliged. See infra at 1405-06.
. "Forfeiture” is "the failure to make the timely assertion of a right” (as opposed to "waiver,” which is “the intentional relinquishment or abandonment of a known right”). Olano, - U.S. at -, 113 S.Ct. at 1777.
. As the district court explained, "It’s simply a matter of' courtesy.... It also keeps [the alternates] from feeling they've sat here for three months and then just kind of get kicked out.” Olano, - U.S. at -, 113 S.Ct. at 1774.
. The court observed there was no reason why a defendant could not waive a violation of Rule 24(c) by consenting to the alternate’s recall, noting
If the defendant would prefer to take his chances with the jury in its reconstituted form rather than undergo the expense and uncertainty of a new trial, why should he not be allowed to? Rule 23(b) allows the parties to stipulate to trial by a jury 'of any number less than 12'; and of course the defendant can if he wants waive all right to a jury trial, see Rule 23(a). No doubt there are limits to waiver; if the parties stipulated to trial by 12 orangutans the defendant's conviction would be invalid notwithstanding his consent, because some minimum of civilized procedure is required by community feeling regardless of what the defendant wants or is willing to accept.
Id. at 588.
. We are cognizant of the fact that the jury had been excused for some seven days, but do not think it would have been too inconvenient nor unmanageable for the court to have summoned juror Dunbar along with the prosecutor and defense- counsel for a short hearing concerning *1412whether juror Dunbar had been subjected to any outside influence.