Michael Darrell Sanders, an Arkansas inmate, appeals from a final judgment entered in the District Court1 for the Eastern District of Arkansas upon a jury verdict awarding him $1 compensatory and $10 punitive damages against prison guard Harry Rhodes and granting judgment to other defendant prison officials in his 42 U.S.C. § 1983 action. Sanders claimed that prison officials failed to protect him from attacks by other inmates. Sanders also appeals an order granting three prison officials summary judgment on the ground of respondeat superior. Rhodes cross-appeals the magistrate judge’s order awarding Sanders attorney’s fees. For the reasons discussed below, we affirm the judgment of the district court.

In his complaint, Sanders, who is white, asserted that after he hit a black inmate *922with a hoe in self-defense at Cummins and was transferred to the Tucker Maximum Security Unit of the Arkansas Department of Correction, other black inmates affiliated with “Muslim power” threatened him repeatedly with bodily harm. He alleged that after he hit two other inmates with a hoe in self-defense, he informed defendants Classification Director Brewer, Warden Norris, Chief Security Officer Perry, Assistant Director Morgan, Director Lock-hart, Board of Corrections members and Chairman Walker, and Governor Clinton of his need for protection.

Sanders further alleged that, while on a work detail guarded by defendants Sergeant Brantley and Major Rhodes, inmate Hardin struck Sanders in the face with a hoe, breaking his jaw. Sanders alleged that the defendant prison officials were deliberately indifferent to his serious need for protection by failing to transfer him or to separate him from others. Sanders sought declaratory and injunctive relief, and compensatory and punitive damages. Sanders also requested a jury trial.

Defendants Walker, Lockhart, and Morgan moved for summary judgment, arguing that their only involvement was their receipt of Sanders’s letters, and that re-spondeat superior was not a basis for relief under section 1983. The magistrate judge2 granted the three defendants summary judgment.

Sanders filed an amended complaint alleging that he told Rhodes he had received additional threats against his life. Despite Sanders’s protest, Rhodes assigned him to the hoe squad with inmate Thompson. Sanders alleged that Thompson attacked Sanders with a hoe and was about to strike a fatal blow to Sanders when a guard shot and killed Thompson.

At the jury trial, Sanders testified in detail about the five hoe-squad incidents that occurred between 1986 and 1991. During cross-examination, the prison officials introduced an audio tape recording of Sanders’s testimony at another inmate’s 1988 trial, which was inconsistent with the testimony he had just given. When Sanders’s attorney objected to having the tape recording played for the jury because he had not yet had an opportunity to listen to it, the magistrate judge called a recess so that the attorney could hear the tape recording. After the recess and out of the presence of the jury, Sanders’s attorney assented to the playing of the tape recording, but requested transcripts because of the poor audio quality. The tape recording was then played for the jurors, each of whom had a transcript. After the tape recording was played, Sanders admitted that he had committed perjury at the 1988 trial.

Three other inmates testified that they heard threats against Sanders’s life. After Sanders’s case-in-chief, the magistrate judge granted a directed verdict in favor of Brantley. The prison officials then presented their case, in which Rhodes, Perry and Brantley testified that they did all they could to prevent the assaults upon Sanders.

The jury returned a verdict for Sanders against Rhodes for $1 in compensatory and $10 in punitive damages, and verdicts for the remaining defendants. Following trial, Sanders moved for attorney’s fees and expenses of approximately $14,000. The prison officials responded that the award should be reduced for partial success because Sanders prevailed against only one of the original eight defendants, he did not obtain injunctive or declaratory relief, and he was awarded only nominal damages. The magistrate judge concluded that the requested fee award should be reduced to $7500 in attorney’s fees and $418.09 in expenses, based on the limited ultimate success at trial. The magistrate judge also granted counsel’s motion to withdraw. This appeal followed.

SUPERVISOR LIABILITY

Sanders first argues that the magistrate judge erred in granting summary judgment in favor of Lockhart, Woodson, and Morgan. He argues that respondeat *923superior is not applicable because these three defendants received actual notice of his need for protection and failed to take any action. “To hold supervisors liable under section 1983, a plaintiff must show that a superior had actual knowledge that his [or her] subordinates caused deprivations of constitutional rights and that he [or she] demonstrated deliberate indifference or ‘tacit authorization’ of the offensive acts by failing to take steps to remedy them.” Pool v. Missouri Dep’t of Corrections & Human Resources, 883 F.2d 640, 645 (8th Cir. 1989) (quoting Wilson v. City of North Little Rock, 801 F.2d 316, 322 (8th Cir. 1986)). A single incident, or a series of isolated incidents, usually will not provide a sufficient basis to assign supervisory liability. Howard v. Adkison, 887 F.2d 134, 138 (8th Cir. 1989).

Defendants Lockhart, Woodson and Morgan are upper-level supervisors. Even assuming that mere receipt of Sanders’s letters constituted sufficient personal involvement to defeat defendants’ summary judgment motion, we conclude that, because the jury did not find the lower-level and more closely-involved supervisors liable, the jury would not have found these three defendants liable on a theory of direct responsibility to supervise. See Beard v. Lockhart, 716 F.2d 544, 545 (8th Cir. 1983) (per curiam).

IMPEACHMENT

Sanders also argues that the magistrate judge erred in admitting the tape recording of his testimony at the other trial because of the unfair surprise. Sanders failed to preserve his objection to the use of his previous trial testimony. After listening to the tape recording, Sanders’s counsel assented to the playing of the tape recording, and thus waived his objection. Even if the objection had not been waived, the evidence was proper impeachment testimony, counsel was permitted to listen to the tape recording before the jury heard it so that he could prepare any objections, and Sanders was permitted to explain any inconsistencies in the testimonies. Thus, the magistrate judge did not abuse his discretion in allowing the tape recording to be played.

ADEQUACY OF JURY VERDICT

Sanders next argues that the judgment should be reversed because the nominal damages award amounted to a refusal to assess damages. The jury award of only nominal damages on this record is troubling; however, Sanders did not file a motion for new trial. Absent exceptional circumstances, the issue of the adequacy of a jury verdict must first be presented to the trial court in a motion for a new trial in order to preserve the issue for appellate review. Haley v. Wyrick, 740 F.2d 12, 13-14 (8th Cir. 1984). Exceptional circumstances may exist where there is a “plain injustice,” or a “monstrous” or “shocking” result. Taken Alive v. Litzau, 551 F.2d 196, 198-99 (8th Cir. 1977). We have carefully reviewed the record, and we find the verdict neither “shocking” nor a “plain injustice.”

ATTORNEY’S FEES

In his cross-appeal, Rhodes argues the magistrate judge abused his discretion in not further reducing the attorney’s fee award because of the limited success Sanders achieved. We disagree. The magistrate judge properly considered the factors for awarding Sanders attorney’s fees under 42 U.S.C. § 1988. Where a plaintiff has “achieved only limited success, the district court should award only that amount of fees that is reasonable in relation to the results obtained.” Hensley v. Eckerhart, 461 U.S. 424, 440, 103 S.Ct. 1933, 1943, 76 L.Ed.2d 40 (1983). Compensation should not be awarded on a claim-by-claim basis, but rather on specific theories of relief. Hendrickson v. Branstad, 934 F.2d 158, 164 (8th Cir. 1991). Based on the magistrate judge’s finding that Sanders’s several claims contained a common theory, we conclude there was no abuse of discretion in the fee determination.' See id. at 162 (fee determination reversible only if court abused its discretion).

*924Accordingly, we affirm the judgment of the district court.