Defendants-appellants Harrison Daniels (Daniels), Patrick Sayes (Sayes), and John Swan (Swan) appeal their respective convictions under 18 U.S.C. § 242. We affirm.

Daniels, Sayes, and Swan were corrections officers at the Louisiana State Penitentiary at Angola (Angola or the prison). They were indicted and convicted in connection with a beating inflicted on Rayfield Jackson (Jackson), a prisoner at Angola, that occurred on or about December 22, 1997. At the time of the incident, Daniels and Swan held the rank of sergeant and Sayes was a lieutenant.2 In essence, the charges against the defendants were as follows: Daniels and Swan committed a brutal battery of Jackson that left Jackson severely injured. Sayes, the supervising officer, witnessed the attack, and willfully permitted and made no attempt to stop it. Following the attack, the three defendants allegedly deprived Jackson of access to medical care. The charges were brought pursuant to 18 U.S.C. § 242.3

An indictment was returned on May 25, 19994 charging the three defendants as follows:

"Count 1: On or about December 22, 1997, in the Middle District of Louisiana, defendants, HARRISON DANIELS and JOHN SWAN, while acting as Corrections Sergeants with the Louisiana State Penitentiary in Angola, Louisiana, under color of the laws of the State of Louisiana, aiding and abetting each other, did willfully assault and beat Rayfield Jackson, resulting in bodily injury to Rayfield Jackson, and did thereby willfully deprive Rayfield Jackson of the right secured and protected by the Constitution and laws of the United States not to have cruel and unusual punishment inflicted upon him.

All in violation of Title 18, United States Code, Sections 242 and 2.

Count 2: On or about December 22, 1997, in the Middle District of Louisiana, defendant, PATRICK SAYES, while acting as a Corrections Lieutenant with the Louisiana State Penitentiary in Angola, Louisiana, under color of the laws of the State of Louisiana, did willfully permit other officers with the Louisiana State Penitentiary in Angola, Louisiana in his presence and under his supervision, namely Corrections Sergeants Harrison Daniels and John Swan, unlawfully to assault and beat Rayfield Jackson, while Rayfield Jackson was in the custody of those officers, and did willfully fail to prevent these unlawful assaults; resulting in bodily injury to Rayfield Jackson, and did thereby willfully deprive Rayfield Jackson of the right preserved and protected by the Constitution and laws of the United States not to be deprived of liberty without due process of law, which includes the right to be kept free from harm while in official custody.

All in violation of Title 18, United States Code, Sections [sic] 242.

Count 3: On or about December 22, 1997, in the Middle District of Louisiana, defendants, PATRICK SAYES, HARRISON DANIELS, and JOHN SWAN, while acting as Corrections Officers with the Louisiana State Penitentiary in Angola, Louisiana, under color of the laws of the State of Louisiana, aiding and abetting one another, did willfully prevent Rayfield Jackson from receiving medical care and treatment, resulting in bodily injury to Rayfield Jackson, and did thereby willfully deprive Rayfield Jackson of the right secured and protected by the Constitution and laws of the United States not to have cruel and unusual punishment inflicted upon him.

All in violation of Title 18 United States Code, Sections 242 and 2." Indictment, Record Excerpts for Daniels at Tab 5.

The three defendants were tried together in the United States District Court for the Middle District of Louisiana. On January 21, 2000, the jury returned a verdict finding Daniels guilty as to Counts 1 and 3, Swan guilty as to Count 1 and not guilty as to Count 3, and Sayes guilty as to Count 2 and not guilty as to Count 3. On May 5, 2000, following a sentencing hearing, the district court sentenced Daniels to ninety-six months in prison, Swan to eighty-seven months in prison, and Sayes to eighty-seven months in prison.

According to the trial testimony, the beating took place sometime on the morning of December 22, 1997.5 On that date, the defendants were assigned to work in the prison's Cuda 1 unit (Cuda). Cuda is a unit or tier within Camp J, the prison's maximum security disciplinary facility. During a given shift, two sergeants are assigned to each unit. The sergeants are under the supervision of a lieutenant who has charge over several units at a given time. A tier consists of a row of fourteen cells separated by concrete walls. A unit has showers and a lobby at one end, followed by cells numbered one through fourteen, with cell 1 being closest to the lobby and cell 14 at the far end. Jackson was housed in Cuda's cell 8.

At trial, defendant Sayes, Jackson, and six other prisoners incarcerated in the Cuda unit testified regarding the events of the morning of December 22, 1997. Each witness had a different vantage point and their testimony diverged with regard to some particulars. But the testimony was generally consistent with regard to several relevant facts, which we now describe. On that morning, defendant Daniels went to Jackson's cell to escort Jackson to the medical clinic to receive an injection.6 Angola policy requires that prisoners in the Camp J facility wear restraints when they are transported and Daniels was carrying a set of metal handcuffs when he approached Jackson's cell. Jackson informed Daniels that, because of a skin condition, he was required to wear plastic "flex cuffs" instead of metal handcuffs. Daniels insisted on using the metal cuffs and the two began to argue through the bars of Jackson's cell. As the argument escalated, Daniels spat a mouthful of sunflower seeds into Jackson's face. Jackson allegedly spat back at Daniels. Daniels then procured a bucket of water and doused Jackson with it.7

Daniels then telephoned Sayes and explained that he needed a set of flex cuffs to restrain Jackson. Sayes arrived at the Cuda tier and brought the flex cuffs to Daniels. Although he now had flex cuffs available, Daniels restrained Jackson with the metal handcuffs.8 Jackson's legs were also shackled and he was restrained with a waist chain around his waist. Jackson was removed from his cell and Daniels began violently kicking and punching Jackson. Sayes witnessed the beating and neither did nor said anything to attempt to stop it. Daniels moved Jackson down the tier, to the lobby, where Swan joined Daniels in attacking Jackson. At one point, Swan apparently struck Jackson forcefully on the side of the head with a shoe. Although Sayes was not indicted for actively participating in the attack, there was testimony that Sayes encouraged the attackers verbally and even struck a few blows himself.

After the beating, Jackson was made to crawl back to his cell on his knees while Daniels continued to taunt and kick him. For several hours, Jackson lay in his cell in severe pain. Daniels apparently prevented a medic from checking on Jackson and did not apprise the officers coming on to the next shift that Jackson had been injured. Jackson finally got medical attention after midnight, nearly fourteen hours after the assault.

Dr. James Hand examined and treated Jackson. Dr. Hand testified that Jackson was brought in shortly after one o'clock on the morning of December 23, 1997. Jackson had severe external and internal injuries, including a collapsed lung, a ruptured kidney, broken ribs, several broken vertebrae, a ruptured eardrum, internal bleeding, and multiple contusions. Dr. Hand testified that, in his opinion, Jackson's injuries were at least ten to twelve hours old and were consistent with a beating occurring thirteen hours before Dr. Hand saw him.

When the extent of Jackson's injuries became known, Angola officials began an internal investigation into the incident. The prison warden offered Sayes immunity for Sayes's statement to the prison investigator. Under the cloak of this immunity promise, Sayes made two statements, one on December 24, 1997, and one on January 13, 1998, to Major Sivula, the official in charge of the prison's investigation. In his statements, Sayes admitted witnessing the attack, identified Daniels and Swan as Jackson's assailants, and described some details of the incident.

After its initial investigation, the prison referred the matter to the FBI. On January 14, 1998, Sivula contacted agent Rondalyn Craft, the FBI agent in charge of the federal investigation. During a telephone conversation, Sivula gave agent Craft some general information about the incident and mentioned Sayes's involvement in it. Sivula and agent Craft testified at a pretrial motions hearing that they did not discuss Sayes's specific statements or the existence of those statements. Agent Craft and another agent, Thomas McNulty, arrived at Angola on January 21, 1998 and began their investigation by reviewing prison log books and other records. They interviewed Jackson and two other prisoners, who corroborated Jackson's account of the incident. Agent Craft also interviewed Dr. Hand. As agent Craft was leaving the prison that day, Sivula provided her with the personnel files of five corrections officers, including the three defendants. Sayes's personnel file contained copies of Sayes's immunized statements. Agent Craft later testified that she was not aware at the time that the statements were in the file and that she never read either statement until January 7, 1999. McNulty testified at the pretrial hearing that he never read the statements. On January 26, 1998, six other FBI investigators interviewed the remaining eyewitnesses and prepared reports based on those statements. These agents also testified at the pretrial hearing that they had no knowledge of the existence or contents of Sayes's immunized statements.

In February 1998, a grand jury heard testimony and indicted Daniels, Swan, and Sayes. Sayes moved to dismiss the indictment, arguing that the Government had unlawfully used his immunized statements, or evidence tainted by receipt of his immunized statements, to support the indictment. To remove any cloud from the indictment, the Government moved to dismiss the indictment without prejudice and the district court granted the motion. The Government then sought a second indictment before a different grand jury. This time the Government presented the grand jury testimony through agent Dan Fontenot, who had no previous connection to the investigation. Agent Fontenot testified at the pretrial hearing that he had no knowledge of the existence or content of Sayes's statements. In his summary testimony to the grand jury, agent Fontenot reviewed agent Craft's written reports of her January 21, 1998, interviews with Jackson, the doctor, and the two eyewitnesses and he presented the reports of the six other FBI agents who had interviewed witnesses. The grand jury returned its indictment of the defendants on May 25, 1999.

The defendants raise several issues on appeal, which we now address.

All three defendants complain that the district court erred in refusing to sever the trial of Sayes from that of Daniels and Swan. Each defendant urged severance in pre-trial motions and the motions were reurged at various points during the trial. Rule 14 of the Federal Rules of Criminal Procedure provides in relevant part: "If it appears that a defendant or the government is prejudiced by a joinder ... of defendants in an indictment or information or by such joinder for trial together, the court may ... grant a severance of defendants or provide whatever other relief justice requires." We review the district court's denial of a motion for severance for abuse of discretion. United States v. Peterson, 244 F.3d 385, 393 (5th Cir.2001). "To prevail, the defendant must show that: (1) the joint trial prejudiced him to such an extent that the district court could not provide adequate protection; and (2) the prejudice outweighed the government's interest in economy of judicial administration." Id. (internal quotation marks omitted).

The defendants argue that they were prejudiced because their defenses were mutually antagonistic and irreconcilable. Sayes testified that he witnessed Daniels and Swan attacking Jackson and that he was so shocked by the brutality of the attack that he was paralyzed into inaction. The core of Sayes's defense was effectively that he did not willfully permit the deprivation of Jackson's rights. Neither Daniels nor Swan testified. Their defense remained ambiguous throughout much of the trial and it ultimately evolved into an argument that the beating did not occur during their shift. The core of their defense was simply that the prosecution had not proved that they were the perpetrators of the beating.

The Supreme Court has explained that "[m]utually antagonistic defenses are not prejudicial per se." Zafiro v. United States, 506 U.S. 534, 113 S. Ct. 933, 938, 122 L. Ed. 2d 317 (1993). Furthermore, even if prejudice is shown, Rule 14 "leaves the tailoring of the relief to be granted, if any, to the district court's sound discretion." Id. To promote judicial economy and the interests of justice, the federal system prefers joint trials of defendants who are properly charged in joint indictments. Id. at 937. "[A] district court should grant a severance under Rule 14 only if there is a serious risk that a joint trial would compromise a specific trial right of one of the defendants, or prevent the jury from making a reliable judgment about guilt or innocence." Id. at 938.

Zafiro teaches that joint defendants face a heavy burden in demonstrating to a district court that antagonistic defenses warrant granting a severance motion. The burden is correspondingly heavier when, on appeal, they seek to demonstrate that the district court abused its discretion by declining to do so. Even prior to the Supreme Court's decision in Zafiro, this court articulated a stringent standard for finding that defenses are so antagonistic as to compel severance: the defenses must be so diametrically opposed that "the jury, in order to believe the core of testimony offered on behalf of [one] defendant, must necessarily disbelieve the testimony offered on behalf of his co-defendant." United States v. Berkowitz, 662 F.2d 1127, 1134 (5th Cir. Unit B 1981). The conflict must concern the core or essence of a defense, not merely "minor or peripheral matters." Id. Even when such a conflict is present, giving rise to the risk of prejudice, the district court should take into account the public interests in judicial economy and the administration of justice served by joint trials and the possibility that limiting instructions or other less drastic measures will suffice to cure any risk of prejudice. See Zafiro, 113 S.Ct. at 938; see also United States v. Matthews, 178 F.3d 295, 299 (5th Cir.1999) ("Severance is not automatically required when co-defendants present mutually antagonistic defenses.").

For several reasons, we hold that the defendants have not shown that the district court abused its discretion by denying their motions for severance. First, it is arguable at best that the defenses in this case were mutually antagonistic under the Berkowitz standard. The core of Sayes's defense was not that Daniels and Swan were guilty of the beating; it was that Sayes was too paralyzed to act when he witnessed a beating, by whomever it was performed. The identity of Jackson's assailants was peripheral to Sayes's "paralysis" defense. The essence of Daniels and Swan's defense was that they were wrongly identified as Jackson's assailants. It is true that, were a jury to conclude that Daniels and Swan were not Jackson's attackers they would be faced with a question regarding Sayes's credibility. But the jury could believe the core of Saye's defense — that he was paralyzed — and still believe that he was mistaken about the identity of the attackers. This possibility would not "compromise a specific trial right" of Sayes, Zafiro, 113 S.Ct. at 938; there is no right entitling a defendant to have his testimony believed. As far as prejudice to Daniels and Swan, Sayes was just one of several eyewitnesses who testified that Daniels and Swan were Jackson's assailants. Dr. Hand's testimony regarding the age of Jackson's injuries was substantial evidence that the beating occurred on Daniels and Swan's shift. And again no specific trial right of the defendants was compromised. In a separate trial, Daniels and Swan could not have asserted a right to prevent Sayes from testifying against them (although Sayes could have asserted his Fifth Amendment right to avoid testifying unless he were tried first).

Even if there were some risk of prejudice here, the district court gave the very limiting instructions that the Supreme Court has approved as usually sufficient to cure this character of prejudice: (1) that the jury must consider the evidence separately and independently for each defendant and each charge; (2) that the government's burden was to prove each defendant's guilt beyond a reasonable doubt; (3) that no inferences must be drawn from a defendant's exercise of the right to silence; and (4) that statements by the lawyers, including opening and closing arguments, are not evidence. See Zafiro, 113 S.Ct. at 939. The district court further instructed the jury that it could choose to believe one portion of a witness's testimony while disbelieving another portion.

Moreover, the judicial economy interest served by a joint trial was particularly strong in this case. Virtually all of the evidence, including witness testimony, derived from the same sources. Most of the witnesses were prisoners or personnel from a maximum security prison. This circumstance created a significant logistical burden that would have been doubled if the severance motions were granted. Further, the defendants did not specifically articulate the conflict they perceived between their defenses until well into the trial, if ever. As late as the close of the prosecution's case, counsel for the defense offered the court only vague and conclusory assertions that the defense theories were in conflict.

All things considered, the district court did not abuse its discretion by denying the motions to sever.

2. The Eighth Amendment/Fourteenth Amendment Issue

We turn now to the next ground for appeal: the contention by Daniels and Swan that the evidence was not sufficient to sustain their convictions because the indictment charged that the assault violated Jackson's Eighth Amendment right to be free of cruel or unusual punishment rather than his Fourteenth Amendment right to due process. Daniels and Swan made motions for acquittal on this ground at the close of the Government's case and at the close of all the evidence. This court reviews the denial of a motion for a judgment of acquittal de novo. United States v. Garcia, 242 F.3d 593, 596 (5th Cir.2001). The evidence is sufficient if, drawing all reasonable inferences and credibility determinations in the light most favorable to the prosecution, a rational trier of fact could have found that the evidence established the essential elements of the crime beyond a reasonable doubt. Id.

Counts 1 and 3 of the indictment, which stated the charges against Daniels and Swan, accused those defendants of depriving Jackson of his right "not to have cruel and unusual punishment inflicted upon him." These terms, of course, echo the language of the Eighth Amendment and the prosecution, during the course of trial, made clear that it was proceeding on an Eighth Amendment deprivation theory. But the essential elements of the offense defined in 18 U.S.C. § 242 do not confine the offense to a deprivation of only some limited subset of constitutional rights. The relevant elements are that a person (1) acting under color of law; (2) "willfully subjects any person ... to the deprivation of any rights, privileges, or immunities secured or protected by the Constitution or laws of the United States." 18 U.S.C. § 242 (emphasis added). An indictment is sufficient to sustain the resulting conviction if "the factual predicate of the indictment is identical to that of the conviction." United States v. Arlen, 947 F.2d 139, 144 (5th Cir.1991); see also United States v. Young, 730 F.2d 221, 224 (5th Cir.1984). In this case, there was no variance between the factual predicate charged in the indictment and that developed at trial. Daniels and Swan were charged with willfully assaulting and beating Jackson and willfully preventing him from receiving medical care, all on or about December 22, 1997. The indictments set forth particular facts sufficient to give these defendants notice of the allegations against them; the "acts and intent" that make up the crime were "set forth in the indictment, with reasonable particularity of time, place, and circumstances." United States v. Cruikshank, 92 U.S. 542, 558, 23 L. Ed. 588 (1875); cf. Stirone v. United States, 361 U.S. 212, 80 S. Ct. 270, 273, 4 L. Ed. 2d 252 (1960) (defendant could not be tried for interference with interstate commerce in steel when indictment charged only interference with interstate commerce in sand); Young, 730 F.2d at 224 (distinguishing Stirone from case in which the facts alleged in the indictment were identical to those facts on which the conviction rested).

If the factual predicate was sufficient to establish a deprivation of Jackson's Fourteenth Amendment due process rights, then it is sufficient to support a conviction under section 242 and that evidentiary sufficiency is not diminished merely because the indictment described the constitutional violation with language drawn from the Eighth Amendment.9 On appeal, Daniels and Swan do not deny that the charged conduct would constitute a Fourteenth Amendment due process deprivation. Indeed, in his brief to this court, appellant Swan expressly concedes that it may constitute such a violation. At any rate, in Valencia v. Wiggins, 981 F.2d 1440 (5th Cir.1993), we explained that a claim of excessive force by a law enforcement officer is correctly examined under the same standard regardless whether the claim arises under the Eighth Amendment or the Fourteenth Amendment. See id. at 1447. In Valencia, we applied the standard developed by the Supreme Court in the context of Eighth Amendment claims involving the use of excessive force against convicted prisoners to the context of a pretrial detainee's claim arising under the Due Process Clause. Id. at 1445-47 (applying Whitley v. Albers, 475 U.S. 312, 106 S. Ct. 1078, 89 L. Ed. 2d 251 (1986) and Hudson v. McMillian, 503 U.S. 1, 112 S. Ct. 995, 117 L. Ed. 2d 156 (1992)). We found that many of the Supreme Court's "concerns in Whitley were not limited to Eighth Amendment claims but `arise whenever guards use force to keep order.'" Id. at 1446 (quoting Hudson, 112 S.Ct. at 998); see also Rankin v. Klevenhagen, 5 F.3d 103, 106 (5th Cir.1993).

In its instructions to the jury, the district court stated: "In order to prove an excessive force violation, the Government must prove that the defendant under consideration unnecessarily and wantonly inflicted pain on an inmate."10 This language mirrors the legal standard affirmed by the Supreme Court in Hudson. Hudson, 112 S.Ct. at 998; see also Whitley, 106 S.Ct. at 1084. Daniels and Swan raise no challenge to this jury instruction on appeal. The defendants rely on George v. Evans, 633 F.2d 413 (5th Cir.1980), in which we stated that "[a]n isolated assault by an individual guard on an inmate is not, within the meaning of the eighth amendment, punishment." Id. at 415. In Hudson, the Supreme Court expressly left open the question whether George correctly stated the law. Hudson, 112 S.Ct. at 1001. In George, we also said, "Whether or not an eighth amendment violation can be established, the use of undue force by a prison guard is actionable as a deprivation of fourteenth amendment due process rights." George, 633 F.2d at 416. As we have explained, a Fourteenth Amendment deprivation may be predicated on the same facts as an Eighth Amendment deprivation. A Fourteenth Amendment violation is sufficient to satisfy section 242's constitutional deprivation element. In any event, the defendants do not contend either that the factual predicate in this case was insufficient to constitute a Fourteenth Amendment deprivation or that the jury instructions were fatally insufficient for that purpose.11

Sayes moved prior to trial to have the May 25, 1999 indictment dismissed, contending that the grand jury heard evidence that was derived from and tainted by Sayes's immunized statements to prison investigators. After reviewing the evidence, the district court denied the motion. On appeal, Sayes contends that the denial of his motion to dismiss was in error. If a defendant shows that he has made immunized statements regarding matters related to the federal prosecution, the Government must establish by a preponderance of the evidence that the evidence relied upon by the grand jury was derived from independent, legitimate sources. Kastigar v. United States, 406 U.S. 441, 92 S. Ct. 1653, 1665, 32 L. Ed. 2d 212 (1972); United States v. Cantu, 185 F.3d 298, 303 (5th Cir.1999). The district court found that the Government had satisfied this burden. This factual finding is reviewed for clear error. United States v. Williams, 859 F.2d 327 (5th Cir.1988).

On appeal, the Government does not contest the district court's findings that both of Sayes's statements made to prison investigators — one on December 24, 1997, the other on January 13, 1998 — were compelled, immunized statements. See Garrity v. New Jersey, 385 U.S. 493, 87 S. Ct. 616, 620, 17 L. Ed. 2d 562 (1967). The Government thus had the burden of proving that its evidence was derived from legitimate, independent sources. We find no clear error in the district court's determination that the Government satisfied this burden. These statements were not put before, or ever mentioned to, the second grand jury (nor, of course, was there any reference to them before the petit jury). The district court found that the ten reports filed by the six FBI investigators were free from any taint as the FBI agents had no knowledge of Sayes's statements or their existence at the time the reports were prepared. The transcripts, which agent Fontenot presented to the grand jury, of the testimony of four eyewitnesses described what those witnesses saw and made no reference to any statement by Sayes. Agent Craft testified that she had not seen or used Sayes's statements in the course of her investigation. Conclusory denials by an FBI agent are not alone sufficient to carry the Government's burden. United States v. Seiffert, 463 F.2d 1089, 1092 (5th Cir.1972). But agent Craft's credibility was for the district court to decide and her explanation was bolstered by an affirmative showing that she relied on independent sources. Cf. id. (a conviction must stand if the Government can affirmatively show that it did not directly or indirectly use immunized testimony). Agent Craft discovered the identities of potential witnesses — the prisoners and guards on the tier — from prison records and log books before she had access to Sayes's immunized statements. Jackson and the other eyewitnesses she interviewed provided her with the names of officers involved, including Sayes, based on their personal knowledge of events.

Sayes was in substantially the same position he would have been in if he had not made any immunized statements.

4. The Exposure of the Prosecution Team to Immunized Statements

Sayes further contends that, even if the indictment was not based on tainted evidence, the fact that the prosecution team was eventually exposed to Sayes's immunized statements required dismissal of the entire prosecution team from the case. Sayes directs our attention to cases from our sister circuits in which a prosecutor's exposure to immunized testimony presented a Kastigar issue, even though the immunized testimony was not directly used at trial. In United States v. McDaniel, 482 F.2d 305 (8th Cir.1973), the Eighth Circuit found that the district court failed to consider "the immeasurable subjective effect" that reading immunized testimony had on the prosecutor's trial preparation. Id. at 312. Therefore, the Government had failed to meet its heavy Kastigar burden of showing that it had made no use of the immunized testimony. Id. Similarly, in United States v. Semkiw, 712 F.2d 891 (3d Cir.1983), the Third Circuit remanded because the district court had failed to make any factual findings regarding whether the prosecutor made any use of the immunized testimony in the preparation and conduct of the trial and thereby prejudiced the defendant. Id. at 895. The Semkiw court stressed that the Government had the burden of proving that it had made no use of the testimony. Id.

Several circuits have expressly disagreed with McDaniel and Semkiw. See, e.g., United States v. Velasco, 953 F.2d 1467, 1474 (7th Cir.1992); United States v. Serrano, 870 F.2d 1, 17 (1st Cir.1989); United States v. Mariani, 851 F.2d 595, 600 (2d Cir.1988); United States v. Byrd, 765 F.2d 1524, 1531 (11th Cir.1985). These courts have emphasized that the mere subjective influence that exposure to immunized testimony may have on a prosecutor's thinking during trial preparation, without more, is too tangential to constitute an impermissible "use" of such testimony. Velasco, 953 F.2d at 1467; Mariani, 851 F.2d at 600. We observe that neither Semkiw nor McDaniel actually adopted a per se rule that any exposure to immunized testimony requires disqualification of a prosecutor. See Semkiw, 712 F.2d at 895 (remanding because the appeals court did not know the extent of the prosecutor's access to immunized testimony, nor the use she may have made of it, and thus was unable to determine whether the defendant had been prejudiced); McDaniel, 482 F.2d at 312 (because of unusual circumstances attending that case, the Government's burden of proof was "virtually undischargeable."). The Eighth Circuit itself has since distinguished McDaniel, limiting it to its "unusual circumstances." United States v. McGuire, 45 F.3d 1177, 1183 (8th Cir.1995) ("The determination of a McDaniel violation necessarily turns on the facts of each case and again focusses on whether the immunized testimony was used by the prosecutor exposed to it.").

To satisfy Kastigar, use immunity must leave the witness in substantially the same position as if he had asserted his Fifth Amendment privilege not to testify. Kastigar, 92 S.Ct. at 1664. There may be some cases in which the exposure of a prosecution team to a defendant's immunized testimony is so prejudicial that it requires disqualification of the entire prosecution team. But this is not such a case. As we have already explained, Sayes's immunized statements contained no relevant information that was not readily available from legitimate, independent sources. It was uncontroverted that Jackson had been beaten. Several eyewitnesses had already told investigators that Sayes was present and did not intervene to stop the beating. Sayes was not charged with participating in the attack, only with observing it and willfully failing to do or say anything in an effort to stop it. Some variation of his "paralysis" defense was Sayes's only effective defense strategy and a competent prosecutor would need no special insight or information to discern this.12 Sayes's defense that he did not "willfully" permit the attack was his only available avenue for minimizing his involvement. We also note that agent Craft testified at the pretrial hearing that in a February 1998 conference with Sayes's attorney, Assistant United States Attorney Menner, the lead prosecutor in this case, and herself, Sayes's attorney revealed to her and Menner, in the words of Sayes's brief on appeal, "the entire substance of Sayes' immunized statements". Craft likewise testified that at that time she had not read either statement.

We conclude that no error is shown in the district court's refusal to disqualify the prosecution team.

Finally, Sayes objects to supplemental instructions that the district court provided in response to questions from the jury during their deliberations. Specifically, Sayes complains that the district court's answers to jury questions regarding the definitions of "unlawful force" and "willfully" unfairly prejudiced Sayes's defense.

When a challenge to jury instructions is properly preserved for appeal, we review the challenged instructions for abuse of discretion. United States v. Dien Duc Huynh, 246 F.3d 734, 738 (5th Cir.2001). "The standard of review applied to a defendant's claim that the jury instruction was erroneous is whether the court's charge, as a whole, is a correct statement of the law and whether it clearly instructs jurors as to the principles of the law applicable to the factual issues confronting them." Id. (internal quotation marks omitted). When a defendant has failed to properly preserve an issue for appeal, this court will only review it for plain error. United States v. Caucci, 635 F.2d 441, 447 (5th Cir.1981). "Plain errors or defects affecting substantial rights may be noticed although they were not brought to the attention of the court." Fed.R.Crim.P. 52(b). Because we find that Sayes's objections to the district court did not properly preserve the issues he now raises on appeal, we review his challenges under the plain error standard.

Soon after the jury began deliberating, the foreman submitted written questions asking the court, "What is the definition of unlawful assault? Is there a definition for reasonable force in handling inmates?" During a colloquy before the jury was brought back into the courtroom, counsel for Sayes expressed the opinion that rereading the court's original charge on the definition of "excessive force" would be a sufficient response. When the jury was recalled, the court reread the excessive force charge and added, among other things, "In Count 1, to use unnecessary force to Rayfield Jackson, or excessive force, or unlawful force, that is all the same thing. He unlawfully permitted it. And we talked about the duties of an officer." After the jury retired, counsel for Sayes made only the following statement: "I have to object to — I'm not quite sure if we answered their question." Sayes's counsel provided no further explanation whatever of the objection and said nothing else. On appeal, Sayes argues that the above quoted portion of the court's supplemental charge, especially the comment "He permitted it," implied that Sayes was guilty and improperly emphasized that Sayes's failure to intervene constituted guilt, regardless of his intent. Cf. United States v. Carter, 491 F.2d 625, 634 (5th Cir.1974) (there may be reversible error when there is a reasonable possibility that a court's supplemental instructions implied guilt).

After further deliberations, the jury submitted a question asking the court to define "willfully" as used in the indictment. In response, the court reread the original charge on "willfulness." At the request of Sayes's counsel, the court incorporated language from the original charge on the deprivation of civil rights that emphasized that the defendants must have acted with a "bad purpose" or "evil motive."13 The court ended its supplemental charge by adding the following paraphrase: As I have told you, it is not necessary that the act was intended specifically to deprive someone of a constitutional right. What the charge is, is that he deprived someone of a right that happens to be a constitutional right, or that he did an act which deprived a person of a constitutional right.

Whether he intended to deprive them of a right is not the question. The question is whether he intended to do an act that did deprive someone of a constitutional right.

After the jury retired, the court asked if there were any objections and counsel for Sayes responded, "I would just object to the court's emphasis on the last part as going beyond the written instruction, about finding that if a person did an act. That would be my objection." On appeal, Sayes argues that the placement of the "bad purpose" or "evil motive" language in the middle of the charge and the "intended to do an act" language at the end unfairly emphasized that portion of the charge that was favorable to the Government.

Sayes's vague objections to the district court did not properly preserve the issues he now raises on appeal. With regard to the excessive force instruction, the objection that the court did not answer the jury's question bears no resemblance to the argument Sayes urges now. With regard to the willfulness instruction, the objection gave no indication as to in what particular the challenged portion was improper or prejudicial to Sayes. Therefore, we review these instructions only for plain error. Caucci, 635 F.2d at 447. When evaluating supplemental instructions to determine whether they were so prejudicial as to impair a substantial right of the defendant, we consider the instructions as a whole, "not word-by-word or phrase-by-phrase," and we view them in light of other instructions already given. Carter, 491 F.2d at 633.

Sayes does not argue that the district court's instructions actually misstated the law, although he contends that the excessive force instruction under-emphasized the intent element. However, the jury later requested further instruction on "willfulness", thus suggesting that it had not lost sight of the intent element. As to the challenged "He unlawfully permitted it," remark, taken in context the more likely understanding of it is that the court was merely paraphrasing the indictment rather than expressing any opinion that Sayes was guilty. Any emphasis resulting from the particular order of phrases in the willfulness instruction appears inadvertent and was not plainly erroneous; the instruction included an adequate statement of the intent element and the requirement of bad purpose or evil motive.

While we do not condone or recommend the particular portions of the supplemental instructions which Sayes challenges, we conclude that he has not demonstrated that the supplemental instructions constituted plain error warranting reversal under the demanding test of United States v. Olano, 507 U.S. 725, 113 S. Ct. 1770, 123 L. Ed. 2d 508 (1993). To meet that test the instruction must not only be erroneous but clearly so, and, in addition, the defendant bears the burden of persuading us that the error was prejudicial rather than the government having any burden to persuade us that it was not. Id. at 1777, 1778. Finally, even if all these requirements are met, this court must further determine that the error "`seriously affect[s] the fairness, integrity or public reputation of judicial proceedings' before it may exercise its discretion to" reverse the conviction. Johnson v. United States, 520 U.S. 461, 117 S. Ct. 1544, 1550, 137 L. Ed. 2d 718 (1997). We are unable to conclude that the complained of portions of the supplemental instructions, properly considered in light of the entirety of each respective set of supplemental instructions as well as against the background of the original charge, constituted not only error but error which was clearly or plainly such. In any event, Sayes has not persuaded us that any such error was prejudicial, and we likewise do not find that any such error seriously affects the fairness, integrity or public reputation of judicial proceedings. We accordingly hold that Sayes's complaints of the supplemental jury instructions present no reversible error.

For the foregoing reasons, we conclude that appellants' respective complaints on appeal present no reversible error in the proceedings below. The convictions and sentences of defendants Daniels, Swan, and Sayes are AFFIRMED.