COFFIN, Senior Circuit Judge.

Plaintiffs-Appellants, Oscar J. Fernandez and Rosa Fernandez contend that the death of their father and husband ("Mr. Fernandez") during a police and FBI shooting was the product of excessive and unreasonable force. They brought suit under 42 U.S.C. § 1983 against three law enforcement officials, the Town of Brookline, and its former police chief. After a twelve-day trial, the jury exonerated all five defendants. On this appeal, the Fernandezes ascribe various errors to the district court and claim the right to a new trial. After careful review of the record, we are satisfied that the trial was a fair one. Accordingly, we decline to disturb the jury's verdict.

I. Background

We supply only those facts necessary to provide context for our decision. A more detailed treatment of the facts appears in our earlier opinion.

On December 26, 1976, plaintiff-appellant Oscar J. Fernandez was kidnapped and held for ransom by Thomas Oses and William Shepard. Ivan Rodriguez, a son of plaintiff-appellant Rosa Fernandez and stepson of Mr. Fernandez, reported the kidnapping to the FBI on the same day.

The next morning, Oses and Shepard, both armed, entered the Fernandezes' apartment. Defendant Leonard, the senior field officer of the Boston office of the FBI, and defendants Murphy and McDermott, Brookline police officers, received notice of the kidnappers' armed entry. Joined by other Brookline police officers, they decided to enter the Fernandez apartment.

Leonard and the police officers rapped on the door of the third-floor apartment and announced "police!" As they entered, kidnapper Shepard grabbed Mr. Fernandez around the neck and put a revolver to his head. The law enforcement officers shouted to Shepard to drop the gun, which he did not do. Officer Murphy thereafter managed to approach Shepard, press his gun into Shepard's abdomen, and fire.

Within the next few seconds, Mr. Fernandez was killed by FBI and police fire. Four bullets struck him in the back, the fifth struck his jaw. Three of the shots were fired by defendant Leonard, who stood facing Mr. Fernandez. The remaining two came from the gun of defendant McDermott, who was positioned behind him.

The matter of what transpired in the moments immediately preceding the shooting was hotly contested at trial. Leonard, Murphy, and McDermott testified that as Shepard fell to the ground, Mr. Fernandez picked up Shepard's revolver, crouched, and began to fan the gun from right to left in front of Leonard and Murphy, as if about to shoot them. According to defendants, they repeatedly ordered him to drop the gun. Only when he failed to do so did they fire upon him.

The trial testimony of Rosa Fernandez and Ivan Rodriguez directly contradicted that of defendants. Mrs. Fernandez and Rodriguez, both of whom were present during the incident, testified that Mr. Fernandez never picked up Shepard's gun and that the defendants shot him in cold blood. This testimony, however, conflicted with statements made by plaintiffs shortly after the shooting, in preparation for the state's prosecution of Oses and Shepard for the kidnapping.

The only other eyewitness who testified about the events leading up to Mr. Fernandez's death was Thomas Oses, whose testimony was utterly contradictory. At one point, Oses stated that Mr. Fernandez had pointed Shepard's gun at Leonard and Murphy and refused to drop it when ordered to do so; at another, he claimed that Mr. Fernandez never held the gun at all.

II. Discussion

Plaintiffs-Appellants contend that the district court committed various errors entitling them to a new trial. We address each of their claims separately.

A. Fraud on the Court

Five days before trial, plaintiffs moved for entry of judgment on the ground that recently discovered evidence demonstrated that an Assistant U.S. Attorney and an FBI agent had, among other things, "bribed and coerced" Thomas Oses into altering his testimony concerning the death of Mr. Fernandez. Plaintiffs moved, in the alternative, to hold the trial in abeyance and to have their misconduct claim decided in an evidentiary hearing. The district court denied both motions.

1. The Underlying Facts

In 1977, at the state trial of Oses and Shepard for the assault and kidnapping of plaintiff-appellant Oscar Fernandez, Oses testified that Mr. Fernandez never held Shepard's gun. Representing himself, Oses argued to the jury that the law enforcement officers present in the Fernandez apartment had "gunned [Mr. Fernandez] down like a dog," and that the kidnapping story was "a big lie" to "cover up for the FBI murder."

In 1985, Leonard received from Oses a letter requesting that he "send the D.A. up to see [Oses]" so that Oses could "tell the truth" about the Fernandez shooting. At that time, Oses was in prison, having served eight years of his life sentence for the 1976 assault and kidnapping. Hearings on his state appeal were due to begin shortly. In the letter, Oses admitted to having "lied all during" his criminal trial. He also stated unequivocally that Mr. Fernandez did, in fact, wield Shepard's revolver in the moments preceding his death. Pursuant to Oses's request, a federal prosecutor and FBI agent visited Oses in prison and obtained from him a sworn statement mirroring the contents of his letter. Shortly after his meeting with the Assistant U.S. Attorney and the FBI agent, Oses was transferred from a maximum to a minimum security prison.

On May 1, 1989, at a pre-trial conference in the present case, plaintiffs informed the district court of their intention to call Oses as a witness. The Assistant U.S. Attorney representing Leonard informed plaintiffs' counsel that Oses would not be a favorable witness. The government described the substance of Oses's 1985 statement and delivered a copy of it to plaintiffs' counsel shortly thereafter.

This turn of events prompted plaintiffs' counsel to open a letter received by him from Oses in 1987 and, apparently, kept under seal ever since. Though addressed to plaintiffs' counsel, the letter was actually to Ivan Rodriguez. In it, Oses claimed to have changed his story concerning the 1976 shooting in exchange for assurances by the federal government that he would be moved to a minimum security prison for the balance of his sentence.

2. Analysis

On the basis of these facts, plaintiffs argued to the court, before trial, that the federal government had engaged in "obstruction of justice, misconduct and abuse of governmental power" in its dealings with Oses. Any judgment rendered in defendants' favor — without curing the government's misconduct — plaintiffs urged, would have to be set aside.

Properly pruned, plaintiffs' allegations amounted to a claim of "fraud on the court." See Aoude v. Mobil Oil Corp., 892 F.2d 1115, 1118 (1st Cir. 1989) ( Aoude II). A "'fraud on the court' occurs where . . . a party has . . . set in motion some unconscionable scheme calculated to . . . improperly influenc[e] the trier [of fact], or unfairly hamper[ ] the presentation of the opposing party's claim or defense." Id. When evidence of a fraud on the court is adduced prior to trial, the district court may fashion an appropriate pre-trial remedy to cure the effect of any misconduct. Id. at 1119. However, the choice of remedy is committed to the broad discretion of the trial court, and we review such decisions for abuse only. Id. at 1117.

In this case, the district court declined to make a pre-trial finding of fraud on the court. It ruled, instead, that the case should go to trial and that plaintiffs' allegations of misconduct ought to be aired before the jury during the examination and cross-examination of Oses. The court also advised plaintiffs to lodge a complaint of governmental abuse with the Department of Justice.

Plaintiffs claim that the court committed reversible error in so ruling. We disagree.

"[T]here are constitutional limits upon the power of the courts, even in aid of their own valid processes to dismiss an action without affording a party the opportunity for a hearing on the merits of his cause." Societe Internationale Pour Participations Industrielles et Commerciales, S.A. v. Rogers, 357 U.S. 197, 209, 78 S.Ct. 1987, 1094, 2 L.Ed.2d 1255 (1958); see also United States v. Pole No. 3172, Hopkinton, 852 F.2d 636, 642 (1st Cir. 1988). Thus, we have held that, when deciding a motion for dismissal on the ground of fraud on the court, the trial court must "carefully balance the policy favoring adjudication on the merits with . . . the need to maintain institutional integrity and the desirability of deterring future misconduct." Aoude II, 892 F.2d at 1118. Dismissal, we have cautioned, is "an extreme remedy, and should not lightly be engaged." Id. Manifestly, the same would be true of a pre-trial motion for judgment such as that sought by plaintiffs here.

In denying plaintiffs' motion, the district court did not abuse its discretion. To the contrary, it forged what strikes us as an acceptable accommodation of competing principles: Plaintiffs were given an opportunity to prove their allegations of misconduct, and defendants received a hearing on the merits.

We likewise find no abuse in the trial court's denial of plaintiffs' request for a pre-trial evidentiary hearing. See Weinberger v. Great Northern Nekoosa Corp., 925 F.2d 518, 527 (1st Cir. 1991) (trial court's decision not to convene evidentiary hearing normally reviewable for abuse). It is well settled that "'motions do not usually culminate in evidentiary hearings.'" United States v. Cannons Engineering Corp., 899 F.2d 79, 94 (1st Cir. 1990) (quoting Aoude II, 892 F.2d at 1120). Where the parties have had a "fair opportunity to present relevant facts and argument to the court," a matter may be "'heard' on the papers" alone. Aoude v. Mobil Oil Corp., 862 F.2d 890, 894 (1st Cir. 1988) ( Aoude I).

Such was the case here. Plaintiffs submitted extensive pleadings and documentary evidence in support of their fraud on the court claim. In addition to Oses's letters to Ivan Rodriguez and Agent Leonard, the court had before it copies of his 1977 trial testimony and his 1985 sworn recantation. It had, as well, the government's written representations that no promise or inducement had been offered Oses and its offer to submit affidavits to this effect on behalf of the Assistant U.S. Attorney and FBI agent who met with Oses in 1985. In denying plaintiffs' request for a hearing, the court stated for the record that it had given these submissions considerable thought.

Finally, plaintiffs contend that, in declining to make a pre-trial finding of fraud, the district court either misunderstood or disavowed its inherent power to do so. See Aoude II, 892 F.2d at 1119 (trial court possesses "inherent power . . . 'to do whatever is reasonably necessary to deter abuse of the judicial process.' ") (quoting Eash v. Riggins Trucking, Inc., 757 F.2d 557, 567 (3rd Cir. 1985)). While the district court did not explain its decision, the reasonable inference to be drawn is that it simply was not persuaded by plaintiffs' pre-trial showing of misconduct.

Arguably, the most damaging evidence adduced by plaintiffs before trial was Oses's assertion (in his letter to Ivan Rodriguez) that his recantation was the product of promises and threats by the "dirty . . . FBI." Also before the court, however, was an array of evidence tending to undermine Oses's credibility and, thus, the reliability of this statement. Most significant, perhaps, was the copy of Oses's letter to Leonard — apparently written before any other contact had been established between Oses and the federal government — in which he admits to having lied at his 1977 trial and that Mr. Fernandez "did in fact pick the gun up and was brandishing it" before he was shot. In that letter Oses also recalls that the law enforcement officers ordered Mr. Fernandez to drop the gun, and that he did not, but, instead "attempted to pull the triger [sic]." The letter strongly suggests, moreover, that Oses, rather than any federal agent, initiated the 1985 meeting of which plaintiffs' complain.

It would have been more than reasonable for the district court to conclude, on the basis of these submissions, that plaintiffs' allegations of misconduct turned on Oses's credibility. By sending them to the jury, the court, we think, quite properly deferred to the "established safeguards of the Anglo-American legal system [which] leave the veracity of a witness to be tested by cross-examination, and the credibility of his testimony to be determined by a properly instructed jury," see United States v. Dailey, 759 F.2d 192, 196 (1st Cir. 1985).

At bottom, plaintiffs' objections appear to rest on little more than the fact that their case depended, in part, upon an incredible witness. Had the district court resolved the misconduct issue before trial and out of the jury's presence, plaintiffs suggest, no evidence relating to the 1985 meeting between Oses and the government would have been admissible at trial. Thus, according to plaintiffs, they might have called Oses to testify in their behalf, along the lines of his original (pre-1985) version of the Fernandez shooting, free from the risk of impeachment by reference to his subsequent recantation. Instead, plaintiffs complain, they were forced to choose between forsaking the testimony of a key witness and having his credibility destroyed by reference to the 1985 statement.

We appreciate plaintiffs' dilemma. However, our review of the record suggests that Thomas Oses, rather than any error in the district court, was to blame for it.

We now turn to the remaining issues raised by plaintiffs' appeal.

B. The Autopsy Photographs

At trial, plaintiffs sought to introduce a set of autopsy photographs of Mr. Fernandez's naked back and torso. Plaintiffs argue on appeal that the district court produced reversible error by (1) excluding the photographs as irrelevant, (2) curtailing plaintiffs' use of the photographs during cross-examination of a witness, and (3) leaving the jury with the impression that the court found plaintiffs' counsel irritating and unprofessional.

1. Relevance

Evidence is relevant if it tends "to make the existence of any fact that is of consequence to the determination of the action more probable or less probable than it would be without the evidence." Fed.R.Evid. 401. We review a district court's relevancy determination for abuse only, United States v. St. Michael's Credit Union, 880 F.2d 579, 600 (1st Cir. 1989), and find none here.

Plaintiffs argue that the autopsy photographs were relevant because they tended to show that four of the five bullets that struck Mr. Fernandez entered his back. The placement of the entry wounds, plaintiffs suggest, demonstrates that, whether or not Mr. Fernandez was holding Shepard's gun before he was shot, he could not have been facing defendants at the time. Thus, according to plaintiffs, the photographs were relevant to the question of whether Mr. Fernandez was shot in self defense or in the exercise of excessive and unreasonable force.

First of all, we doubt whether, unless instructed, lay persons could distinguish entry from exit wounds in the photographs. Having viewed the photographs ourselves, we are left with the strong suspicion that they could not. The pictures reveal nothing more than the fact that Mr. Fernandez suffered multiple bullet wounds before he died.

More important, we observe, as well, that plaintiffs possessed independent, conclusive evidence that Mr. Fernandez was shot in the back, rather than the chest. For example, plaintiffs introduced at trial a copy of the autopsy report concerning Mr. Fernandez's death. The report describes the location of the entry wounds on Mr. Fernandez's back in scrupulous detail. Thus, even were we to find error in the court's relevancy determination, which we do not, we would be bound to hold it harmless on this record. See Pinkham v. Maine Cent. R.R. Co., 874 F.2d 875, 881 (1st Cir. 1989) ("[e]xclusion of evidence in a jury case constitutes harmless error if the evidence . . . though properly admissible is of a fact already established by other unrebutted evidence and may therefore be regarded as cumulative."); see generally, Fed.R.Civ.P. 61 (error in either admission or exclusion of evidence is grounds for disturbing a judgment only where refusal to do so is inconsistent with substantial justice); Fed.R.Evid. 103(a) (same).

2. Murphy's Memory

On the heels of the court's suppression ruling, plaintiffs attempted to use the photographs while cross-examining defendant Murphy. Murphy had testified that he fired his gun at Mr. Fernandez's chest. Plaintiffs sought to impeach this testimony by eliciting from Murphy the fact that all but one of defendants' bullets had struck Mr. Fernandez in the back. Murphy admitted to having seen Mr. Fernandez's body at the morgue after the shooting. He could recall seeing bullet wounds on the torso, but was unable to say whether the body was facing up or down at the time. When pressed by counsel, Murphy insisted that he could remember nothing more about the body or the bullet wounds. At that point, plaintiffs' counsel informed the court that he "would like to have the photographs." The court responded by threatening to hold counsel in contempt for revisiting the subject of the photographs. Counsel then requested a side bar and attempted to "make an offer of proof," at which point the court dismissed the jury and reprimanded counsel, out of the jury's presence, for attempting to reargue the admissibility of the photographs.

The record is unclear as to the purpose for which plaintiffs hoped "to have the photographs." If, as the district court concluded, plaintiffs were seeking merely to reargue the admissibility of the photographs, the court — having already addressed the merits of the issue — was well within its rights to deny the request. If, on the other hand, as plaintiffs argue in their reply brief, they sought to use the photographs for the limited purpose of refreshing Murphy's memory as to the location of the bullet wounds on Mr. Fernandez's torso, the district court's ruling may have been in error. See 20th Century Wear, Inc. v. Sanmark-Stardust, Inc., 747 F.2d 81, 93 n. 17 (2d Cir. 1984) (use of extrinsic evidence to refresh witness's present recollection is permissible); National Labor Relations Bd. v. Federal Dairy Co., 297 F.2d 487, 488 (1st Cir. 1962) (same); 3 J. Wigmore, Evidence § 758 (1970 Supp. 1991) (same).

Once prompted by the sight of the photographs, plaintiffs contend, Murphy might have been able to recall the location of Mr. Fernandez's entry wounds, as he saw them at the morgue within hours of the shooting. By precluding the use of the photographs during Murphy's cross-examination, the district court thus may have deprived the jury of critical evidence that Mr. Fernandez had been shot in the back.

Whatever the merits of this argument, plaintiffs have not (nor could they have on this record) carried their burden of proving harm. As we already have pointed out, the jury had before it independent, incontrovertible evidence that Mr. Fernandez was shot in the back four times. It is therefore inconceivable that plaintiffs suffered substantial prejudice as a result of their inability to develop the same evidence during Murphy's cross-examination. See discussion supra at 465.

3. Judicial Intemperance

After rebuking counsel and then dismissing the jury, plaintiffs suggest, the court created the impression that plaintiffs' counsel would be sanctioned during the recess. Plaintiffs maintain that by failing to inform the jury, upon its return, that no such punishment occurred, the court improperly left it with the impression that counsel had been formally disciplined. According to plaintiffs, the court's hostility to counsel "conveyed a negative impression o[f] the merits of plaintiffs' case" to the jury, producing reversible error. We find this argument to be without merit.

We do detect strains of impatience, if not irascibility, in the district court's manner during this exchange. However, we cannot say that plaintiffs were substantially prejudiced as a result. As we recently have stated, the fact "that a judge may have exhibited a bit of ire or manifested some impatience at times" is, without more, an insufficient basis for finding prejudice. United States v. Devin, 918 F.2d 280, 294 (1st Cir. 1990) ("'Though we expect a trial judge to be sensitive to the judicial role and to exercise restraint, we have no right to anticipate that he will function as . . . [a] bloodless automaton.'") (quoting United States v. Polito, 856 F.2d 414, 418 (1st Cir. 1988)). "In the last analysis, litigants are entitled to a fair trial, but not necessarily a perfect or a monochromatic one." Id. Having scrutinized the court's rulings concerning the autopsy photographs and found them to be sound in substance, we conclude that its occasional lapses in restraint did not deny plaintiffs a fair trial.

C. Rodriguez's Convictions and the Cache of Weapons

Before trial, plaintiffs moved in limine to exclude from evidence two prior narcotics convictions of Ivan Rodriguez (from 1971 and 1975) and testimony concerning a cache of firearms and ammunition seized from the Fernandez apartment in 1970. Plaintiffs contended the evidence was irrelevant and unduly prejudicial — that it would serve only to tarnish the reputation and credibility of the Fernandez family. The court denied plaintiffs' motions and admitted the evidence for the limited purpose of proving defendants' state of mind. On appeal, plaintiffs contend that the court committed reversible error.

We earlier have noted that relevancy determinations will be disturbed only upon a finding of abuse, St. Michael's Credit Union, 880 F.2d at 600. Defendants argued to the district court that their knowledge of Ivan Rodriguez's criminal record and the seizure of weapons was relevant to show their belief that this was not an ordinary kidnapping and that, in entering the Fernandez home, they faced a particularly great risk of a dangerous encounter.

In a case such as this, alleging excessive and unreasonable force, liability depends upon whether the defendants' actions were "reasonable in light of the facts and circumstances confronting them" at the time of the incident. See Graham v. Connor, 490 U.S. 386, 397, 109 S.Ct. 1865, 1872, 104 L.Ed.2d 443 (1989); Dean v. City of Worcester, 924 F.2d 364, 367 (1st Cir. 1991). We have little trouble seeing how defendants' knowledge both of the cache of weapons seized from the Fernandez home and Rodriguez's criminal history might have informed their judgment at the time in question. See Dean, 924 F.2d at 367-69 (police officer's belief that plaintiff was an escaped felon is relevant to determination of whether excessive and unreasonable force was used). Accordingly, we decline to disturb the district court's relevancy ruling.

The court's balancing of the probative value of this evidence against its prejudicial effect, on the other hand, gives us some pause. Evidence is excludable if "its probative value is substantially outweighed by the danger of unfair prejudice." Fed.R.Evid. 403. We agree with plaintiffs that the contested evidence was prejudicial to them. Whether it was unfairly so and whether such prejudice substantially tipped the scales in favor of suppression, however, is a closer question.

Defendants adduced at trial an array of evidence from which the jury might have concluded — without ever hearing of the illegal weapons or Rodriguez's prior convictions — that the Fernandez kidnapping presented an unusual case, and that defendants reasonably anticipated a dangerous confrontation on the morning in question.

This amount of "state of mind" evidence would tend to diminish the likelihood that the challenged items had particular probative value. Were we to find substantial and unfair prejudice, we might conclude that the district court improperly admitted the prior convictions and information relating to the cache of weapons.

By the same token, though, the evidence may be viewed as cumulative, and therefore not unfairly prejudicial. Conceivably, the evidence of the Fernandezes' rather lukewarm cooperation with the FBI and of their relationship with one of the kidnappers, see supra note 11, would have damaged the family's reputation, with or without amplification by the prior convictions and the cache of weapons.

Our review of a district court's weighing of the probative value and prejudicial effect of evidence is notoriously constrained. See Pinkham v. Burgess, 933 F.2d 1066, 1071 (1st Cir. 1991) ("'Only rarely — and in extraordinarily compelling circumstances — will we, from the vista of a cold appellate record, reverse a district court's on the spot judgment. . . .' ") (quoting Freeman v. Package Machinery Co., 865 F.2d 1331, 1340 (1st Cir. 1988)). This is especially so where, as here, the record admits of more than one reasonable interpretation. Extending the district court's decision the great deference it deserves, and finding no harm after reviewing the record as a whole, we must affirm.

D. The Post-Judgment Motions

Following a twelve-day trial, and roughly an hour of deliberation, the jury returned a verdict for the defendants. Plaintiffs subsequently moved for relief from the adverse judgment and for a new trial under Fed.R.Civ.P. 59 and 60(b)(3) and (6). The district court denied both motions.

The Fernandezes contend that their motions should have been granted on the basis of the alleged errors addressed by us in Parts II A-C of this opinion, and because the jury verdict in favor of the municipal defendant, the Town of Brookline, was against the weight of the evidence.

The decision to grant or deny a motion under Rule 59 or 60 is committed to the wide discretion of the district court and must be respected absent abuse. United States v. Boch Oldsmobile, Inc., 909 F.2d 657, 660 (1st Cir. 1990); MacQuarrie v. Howard Johnson Co., 877 F.2d 126, 131 (1st Cir. 1989). To the extent that plaintiffs' motions were predicated upon allegations of error in the various evidentiary and misconduct-related rulings at trial, our discussion at Parts II A-C of this opinion compels the conclusion that they were properly denied.

We likewise are satisfied that the district court properly rejected plaintiffs' attack on the verdict for the Town of Brookline. As this court repeatedly has stated, we will reverse a court's decision not to grant a new trial "'only if the verdict is so seriously mistaken, so clearly against the law or the evidence, as to constitute a miscarriage of justice.' " MacQuarrie, 877 F.2d at 131 (quoting Levesque v. Anchor Motor Freight, Inc., 832 F.2d 702, 703 (1st Cir. 1987)).

Plaintiffs sought to establish § 1983 liability against Brookline on the theory that Mr. Fernandez's death resulted from its "failure to provide hostage training to the members of its police force." The town defended itself on the ground that plaintiffs had failed to prove, among other things, "a direct causal link," City of Canton, Ohio v. Harris, 489 U.S. 378, 109 S.Ct. 1197, 1203, 103 L.Ed.2d 412 (1989), between the alleged failure to train and any constitutional deprivation suffered as a result of Mr. Fernandez's death. See id. at 1205 ("a municipality can be liable under § 1983 only where its policies are the 'moving force [behind] the constitutional violation.'") (quoting Polk County v. Dodson, 454 U.S. 312, 326, 102 S.Ct. 445, 454, 70 L.Ed.2d 509 (1981)).

Having reviewed the record ourselves, we can discern no basis for disturbing the Brookline verdict. Plaintiffs adduced no meaningful evidence of causation, while the town presented evidence tending to preclude such a finding. Most significant, we think, was testimony to the effect that — whatever the level of training provided by the town — the defendant police officers, at all times relevant to plaintiffs' suit, were acting under the supervision of FBI Agent Leonard, a trained and experienced expert in hostage situations. We conclude that the verdict in favor of the town was neither contrary to the weight of the evidence, nor otherwise "seriously mistaken." Accordingly, we sustain the district court's denial of plaintiffs' post-judgment challenge to it.

The judgment of the district court is affirmed.