Defendant Raymond Moreno, Jr., appeals his conviction in the district court for possession of an unregistered firearm, 26 U.S.C. § 5861(d), and of ammunition by a convicted felon, 18 U.S.C. § 922(g)(1). Moreno argues that evidence was lacking to support the verdict; that the court erred in admitting what he characterizes as evidence of “prior bad acts;” and that comments by the prosecutors to the jury deprived him of a fair trial. For the reasons that follow, we affirm Moreno’s convictions.
I.
Moreno first argues that the evidence introduced at trial was insufficient. Our inquiry is a limited one: to decide whether there was evidence from which a rational trier of fact could have concluded beyond a reasonable doubt that Moreno possessed the firearm and the ammunition. Legitimate inferences must be drawn, and credibility determinations resolved, in favor of the verdict. See United States v. Angiulo, 897 F.2d 1169, 1197 (1st Cir.), cert. denied, 498 U.S. 845, 111 S.Ct. 130, 112 L.Ed.2d 98 (1990).
From the government’s evidence at trial (Moreno presented no evidence of his own), *945a reasonable jury could have found the following. On the evening of April 18, 1991, a group of five law enforcement officers, while on foot patrol in the Lenox Street Housing Development in Boston, Massachusetts, heard a series of gunshots coming from another area within the development. Three of the officers, Officers Garvey, Perkins and Devane, ran in the direction of the shots; the other two, Officer Murphy and Trooper Drummy, returned to their parked cruisers.
As the three officers were running down Hammond Street in the direction of the shots, they observed three black males, all wearing black hooded sweatshirts or jackets, emerge from a courtyard in the direction of the gunshots, run across Hammond Street and disappear near a cluster of buildings across the street. One of the officers described the three men as running in a line in a “hunched over” manner. There was only the briefest interval when the defendants together disappeared from view. Almost at once, two of the three officers, joined by Officer Murphy (who had left his cruiser to assist in the foot pursuit), saw the same three men running through a parking lot behind the cluster of buildings, and gave chase.
The officers then saw one of the three men veer off from the other two and run in a separate direction. The second and third men were then seen by the officers to come together briefly and appeared to pass an object between them. Officer Murphy, who was closest to the two individuals, described the item being exchanged as a dark object about one to one-and-a-half feet long. The individual who took this object then ran off through a grass courtyard. The individual who passed on the object immediately stopped, raised his arms and surrendered. That individual was later identified as the defendant, Raymond Moreno, Jr.
Officer Garvey, in order to cut off any escape route, had circled around to the opposite end of the grass courtyard. Officer Garvey soon saw a black male wearing a black hooded sweatshirt enter the courtyard from the area in which Moreno had just been arrested. After telling the man several times to stop, Officer Garvey saw the man make a gesture as if to throw an object aside, and then heard a soft thud on the ground nearby. The man was arrested and identified as Frederick Hardy, who was tried and convicted along with Moreno but is not a party to this appeal. A search of the area revealed a .32 caliber pistol about five to eight feet from where Hardy stopped and made the throwing gesture.
When arrested, Hardy was not in possession of the foot-long object that the officers had seen him receive from Moreno. The officers then searched the path between the area of Moreno’s arrest and the spot at which Officer Garvey first observed Hardy. Hidden in bushes along that direct route, the officers found a double-barrelled sawed-off shotgun with a 12 ¥2 inch barrel, fully loaded with ammunition. This is the firearm and ammunition which Moreno is charged in this case with having possessed.
While Moreno and Hardy were being arrested, Officer Devane was in search of the first of the three runners, who had gone off in a separate direction. Officer Devane discovered a black male, sweating and out of breath and wearing a black hooded sweatshirt, hiding in some bushes. After arresting the individual and placing him in a cruiser, Officer Devane found a semiautomatic pistol on the ground near where the individual had been hiding. The pistol was in the lock-back position, smelled of gunpowder, and was out of ammunition, indicating that it recently had been discharged. The arrested individual was identified as Steven Fernandes.
Several officers then went back to a central courtyard in the middle of the Lenox Housing Development. This courtyard was in the general area of the gunshots, and it was immediately accessible from the spot where the three arrested men were first observed by the officers. In the courtyard, the officers found discharged cartridge casings. These spent casings were matched by a ballistics expert to the pistol that was found next to Stephen Fer-nandes.
*946At the police station after his arrest, Moreno, after receiving his Miranda warning, denied knowing either Hardy or Fer-nandes. He claimed that he had been standing alone in the housing development when he heard shots and started running. At trial, however, a resident of the housing development testified that he had seen Moreno together with Hardy and Fer-nandes a number of times over the prior year. In addition, Officer Dreary of the Boston Police testified that in March 1991 he stopped a red Isuzu Trooper; Hardy was the driver and Moreno was a passenger in the front seat.
We think a reasonable jury could conclude beyond a reasonable doubt from this evidence that Moreno possessed the sawed-off shotgun and its ammunition. Officer Perkins testified that he “saw [the two men] meet and ... could see them having some kind of exchange,” but he was not close enough to describe the object. Officer Murphy, who was closer to the men, did observe the object — which he described as “about a foot and a half [long]” and “dark in color.” It was found directly in the path Hardy took after the exchange with Moreno, prior to his apprehension by Officer Garvey. Once the police testimony is credited, Moreno is effectively tied to the loaded shotgun.
The direct evidence as to the shotgun was reinforced by other evidence. First, Moreno and the individuals seen running away were fleeing from an area in which shots had been fired — shots that the jury could infer had been fired by one of the group, since a pistol belonging to one of the three matched shell casings found in the area of the gunshots. Second, Moreno’s false denial after his arrest of a prior relationship with Hardy and Fernandes suggests a guilty mind and helps rebut any inference that he was merely in the wrong place at wrong time. The direct evidence, bolstered by these secondary inferences, was more than enough to support the jury’s verdict.
II.
Next, Moreno argues that the trial court committed error by allowing the government to introduce evidence of the gunshots heard by the officers prior to Moreno’s arrest, the semi-automatic pistol found with Fernandes and the spent shell casings matching that pistol. Describing the evidence as proof of “other crimes” under Fed.R.Evid. 404(b), Moreno argues that this evidence related only to his character or propensity to commit crime rather than to any legitimate issue in the ease. Rule 404(b) provides that evidence of “other crimes, wrongs or acts” is not admissible to prove “the character of a person in order to show action in conformity therewith.” Such evidence is not prohibited, however, if offered for “other purposes.” Fed.R.Evid. 404(b). See United States v. Rodriguez-Estrada, 877 F.2d 153 (1st Cir.1989).
In this case, the government’s evidence of the gunshots, Fernandes’ pistol, the matching spent ammunition, and Hardy's weapon supports a chain of inferences independent of any tendency of the evidénce to show bad character. The evidence permits the inference that Fernandes, with Hardy and Moreno in attendance, was the individual who discharged the gunshots, and that the three men were running together from the scene of that discharge when first observed by the officers. In turn, the facts that Fernandes and Hardy were armed and that the three men were fleeing together after Fernandes had discharged three rounds of ammunition made it somewhat more likely that the object Moreno was seen to pass along to Hardy was indeed the shotgun later found nearby. See, e.g., United States v. Currier, 821 F.2d 52, 55 (1st Cir.1987) (the proffered evidence of other bad acts was “closely intertwined with the charged offense of possession, providing both significant contextual material and proof that the defendant possessed the gun”).
An example may be of help in understanding the inference. If a defendant were charged with shooting a guard in the course of a bank robbery, it would surely be permissible to show that he was caught fleeing from the scene of a just-robbed bank with two other persons who both pos*947sessed weapons. The defendant could certainly argue to the jury that he was an innocent bystander who was fleeing from a dangerous scene. But the fact of the bank robbery and the possession of the weapons by others arguably associated with the defendant would surely be relevant evidence that the jury could consider along with other evidence against the defendant. If the other evidence included some eyewitness testimony that the defendant had run with the others and had appeared to be carrying a weapon, the facts would not be far from our case.
Indeed, not only are the gun shots and other weapons relevant to the government’s case against Moreno but the ordinary risks presented by Rule 404(b) evidence are especially tame in this case. The hand-guns were not found with Moreno but with other defendants and the gun shots were apparently fired by Fernandes. In other words the evidence suggested “other crimes” not by Moreno but by Fernandes and Hardy. The usual taint of “other crimes” evidence — the risk that the jury will think the defendant a bad man because he committed other crimes — was, so far as it threatened Moreno, largely absent. If the jury otherwise thought him an innocent bystander, it had no reason to attribute to him the crimes of Fernandes and Hardy.
Of course, if the jury accepted the officers’ testimony, it could conclude that Moreno was not a bystander innocently fleeing from danger but rather was associated with the other defendants, had run with them, had handed off his own weapon to Hardy, and had after his arrest falsely denied knowing the other two. If so, the evidence of gunshots furnished the occasion and context for the flight by all three defendants; and the weapons possessed by the other two made it more likely, if only slightly, that Moreno too might be armed. At least the jury was entitled to consider the evidence of gunshots and other weapons and draw such inferences if it chose to do so.
In short, the evidence was clearly admissible on a theory entirely separate from any light it might cast upon Moreno’s “character.” Whether the relevance of such evidence is substantially outweighed by its prejudicial effect is a judgment largely within the broad discretion of the trial judge. Fed.R.Evid. 403; United States v. Simon, 842 F.2d 552, 553 (1st Cir.1988). A defendant is entitled on request to a limiting instruction, warning the jury not to draw the forbidden inference of bad character. Fed.R.Evid. 105. Moreno’s counsel in this case did not seek such an instruction, requesting only a far broader one to which he was not entitled.1
III.
The most troubling aspect of this appeal concerns statements made by the government during argument to the jury. In his opening remarks, the prosecutor stated, “[T]he evidence will show that [the police officers] were doing their jobs protecting the community that has been plagued by violence, senseless violence, shootings and killings. That’s why they were there and that’s why we’re here today.”
There was, of course, no evidence in this case of “senseless violence” or “shootings and killings,” and it was patently improper for the prosecutor to make these remarks to the jury. The argument, playing upon the jury’s emotional reaction to neighborhood violence, was outside the bounds of legitimate argument and cannot be condoned. See United States v. Johnson, 952 F.2d 565, 574 (1st Cir.1991) (admonishing “prosecutorial commentary serving no purpose other than to inflame the passions and prejudices of the jury, and to interject issues broader than the guilt or innocence of the accused” (citations and internal quota*948tions omitted)), cert. denied, — U.S.-, 113 S.Ct. 58, 121 L.Ed.2d 27 (1992).
We do not believe, however, that reversal is warranted. The experienced trial judge, who was in the best position to appraise the prejudicial impact of the prosecutor’s remark, thought a curative instruction the correct remedy. When objection was made, at the end of the prosecutor’s opening, the trial judge forcefully cautioned the jury:
I must give you some instructions to disregard some of the things that were said in the opening statement. There were references to violence in the area, to other incidents in the area than those that are the subject matter of this trial. I will instruct you to disregard all of those references. Some were made very early in the opening statement, others were made in the course of it and toward the end of the opening statement. We are here to try on the evidence with respect to the charges against these defendants, only the charges against these defendants. It is not your function or the function of the court or anyone else to be concerned about anything other than the charges against these defendants and the evidence bearing upon that. You will erase from your mind the arguments about other violence, and the phrase “senseless killings” was used. Those are not matters to be considered by you as you weigh and evaluate the evidence that relates to this case.
We think that this powerful and contemporaneous instruction was adequate to dispel any prejudice caused by the prosecutor’s remarks. See United States v. Giry, 818 F.2d 120, 134 (1st Cir.), cert. denied, 484 U.S. 855, 108 S.Ct. 162, 98 L.Ed.2d 116 (1987).
What is no less disturbing is that, even after the warning embodied by this instruction, the prosecutor again departed from the straight and narrow in his closing. In the course of arguing that the shotgun was not just tossed away but deliberately concealed, the prosecutor — apparently carried away — continued: “Forget about the fact that maybe Mr. Hooker [who lived nearby] or his wife or his three kids might come out and look at the gun and get their heads blown off.” The court then gave a lengthy curative instruction, and the case proceeded. The curative instruction was rather oblique on this issue but it was lengthy, and we are satisfied that the jury got the message to ignore what had just been said.2
If we thought that this second foray was deliberate, there might well be a basis for reversal as a deterrent for the future, see United States v. Capone, 683 F.2d 582, 586 (1st Cir.1982), even though this remark did not directly relate to Moreno for nothing in the evidence suggested that Moreno had carelessly concealed the weapon where Mr. Hooker or his family might find it; that was the act of another defendant. In context, however, the prosecutor’s remark does not appear to have been a deliberate disregard of the court’s earlier, implied warning. Rather, although improper it was seemingly a sudden expression of indignation at the tail-end of a legitimate larger point.
Finally, in appraising possible prejudice, we do not ignore the fact that the case against Moreno was ample. As we said in Giry, 818 F.2d at 133, “prejudice that survives the charge is deemed less likely to have affected the outcome of the trial where strong evidence supports the prosecution’s case”. Here, both judges who join in this majority opinion have independently reviewed the transcripts of the trial testimony in this case, in addition to the briefs; and both are satisfied that the case against Moreno was quite strong and that the objectionable remarks, in context and in light of the instructions given by the trial judge, would not have swayed the jury.
As the evidence already recited shows, Moreno was directly identified by two po*949lice officers as running from the area after gunshots. He was seen by one of the officers to hand over a foot-long object to a second man, and the sawed-off shotgun in question was found near the path where the third one had run shortly before he too was apprehended. This evidence was coupled with other evidence showing the possession of weapons by Moreno’s companions, their flight together with Moreno, and Moreno’s denials that he knew the other two — denials proved to be false by two different witnesses.
The trial of this relatively simple case stretched over 10 days. The trial time was devoted entirely to government evidence, since the defendants did not testify and presented no witnesses of their own. The government put on 21 witnesses, including five officers who were present at the time that Moreno was pursued and whose key testimony has been summarized above. We also note that, although this does not excuse the government’s missteps, defense counsel made arguments before the jury that were not beyond criticism, including cross-examination inappropriately injecting racial issues into the case. In sum, the government’s case was substantial and the imperfections in counsel’s rhetoric were not all on one side.
On balance, we are convinced that the prosecutor’s missteps did not deprive Moreno of a fair trial or a just outcome. The prosecutor’s improper remarks were by and large aberrations, met by prompt countervailing instructions, in a 10-day trial that was otherwise consumed by a detailed exposition of the events of April 18, 1991. This court has found that even more objectionable statements by prosecutors did not warrant reversal where a corrective instruction was given, e.g., Giry, 818 F.2d at 120 (argument comparing charged drug offenses to an “agree[ment] to kill the judge”), or no timely objection was made, e.g., United States v. Machor, 879 F.2d 945, 955 (1st Cir.1989) (drugs “poisoning our community, and our kids die because of this”), cert. denied, 493 U.S. 1094, 110 S.Ct. 1167, 107 L.Ed.2d 1070 (1990). The district court acted within its discretion in this case in concluding that the prosecutor’s misstatements did not so “poison[] the well” as to require a new trial. United States v. Mejia-Lozano, 829 F.2d 268, 274 (1st Cir.1987).3
Nevertheless, for the sake of future cases, we think this worth saying: inflammatory comments to the jury are not only bad tactics in the case at hand but, especially if repeated after warnings, will exhaust the patience of the court and gradually undermine the reputation of the prosecutor’s office. Trials, to be sure, are hard fought contests where not every remark can be carefully weighed. But for the government in a criminal case, fairness is more important than victory. Although we view the evidence as far more substantial than does our dissenting colleague and have some (but not blind) faith in corrective instructions, the government would do well to take this warning seriously.
Affirmed.
. Asked what limiting instruction he would like, Moreno’s counsel asked for one telling the jury that evidence of Fernandes' pistol and the spent shell casings "is not to be considered against the case of Mr. Moreno” or "in no way can be used by this jury” against Moreno. Since the evidence could properly be used against Moreno, the district court quite properly refused this instruction.
. The judge was, at the same time, cautioning the jury to give no weight to any personal opinions expressed by the prosecutor, then or earlier. After completing the curative instruction, the judge gave the lawyers the opportunity to ask for more, and neither requested any addition.
. We have reviewed the other remarks of the prosecutor objected to by Moreno, including the distinct claims that the prosecutor disparaged defense counsel and engaged in improper expressions of personal belief. In some instances, we think the prosecutor made permissible arguments and in others, all milder than the two discussed in text, we think the curative instructions given were adequate.