Herman Kimble Carter, Jr. appeals from his conviction under 18 U.S.C. Sec. 1111 of second-degree murder on property under federal jurisdiction. He claims that the District Court1 committed reversible error by (1) admitting a statement allegedly obtained in violation of his Fifth Amendment privilege against self-incrimination, (2) admitting an alleged hearsay statement, and (3) failing to put three requested voir dire questions to the jury panel. We affirm.

Carter is an inmate at the United States Medical Center for Federal Prisoners at Springfield, Missouri. Beginning in June 1985, a mutual animosity developed between Carter and another inmate, William Miller. Miller allegedly taunted and threatened Carter every time they met, and Carter tried to avoid him. On August 27, 1985, Carter encountered William Miller in the weight room at the Center and they began to fight. Carter drew a razor blade, but Miller wrestled him to the floor and disarmed him. Carter was cut on his hand before several inmates separated them. Carter testified that he then thought he saw Miller take a knife from an ally. This testimony was not corroborated. When Miller turned toward Carter again, Carter picked up a twenty-five-pound barbell and advanced to meet him. After Miller said that Carter would not use the barbell, Carter struck Miller with the bar. Miller immediately collapsed to the ground, where Carter hit him two or three times more before fleeing the weight room. Two of the blows crushed Miller's skull, and he was dead by the time medical assistance arrived.

Carter was indicted for murder in the first degree. Six inmates witnessed the blows and testified against Carter. At trial Carter admitted striking the victim but claimed that he had acted in self-defense because Miller allegedly had a knife. The jury rejected the defense but found Carter guilty only of second-degree murder as a lesser-included offense.

About two hours after the incident, an FBI agent interrogated Carter in his cell. The agent identified himself and gave proper warnings under Miranda v. Arizona, 384 U.S. 436, 86 S. Ct. 1602, 16 L. Ed. 2d 694 (1966), but he misled Carter about the subject of the interrogation. At the beginning of the interview, the agent told Carter that he was investigating an assault, even though he knew that Miller had died and that the investigation was for murder. The agent admitted the deception at trial and stated that he misled Carter "because if you say to a suspect right off the bat, I am talking to you about a murder, he'd be less apt to respond to you." Transcript on Appeal (Tr.) at 138. With one arguable exception,2 Carter consistently testified that he did not know Miller was dead when the interview began. Carter waived his Miranda rights and gave the agent a false alibi that he hoped would place him at a location other than the weight room at the time of the incident. As soon as the agent told Carter that Miller had in fact died, Carter invoked his rights to remain silent and to have counsel present during questioning. The interrogation then ceased.

The agent testified to Carter's false alibi statements during the government's case-in-chief, and they were used primarily to impeach the credibility of Carter's later testimony that he acted to defend himself. Carter claims that these statements should have been suppressed because they were involuntary and used in violation of his privilege against self-incrimination. His theory is defective consent: but for the deception he would not have volunteered the false alibi. He argues that admitting the agent's testimony prejudiced his claim of self-defense, which depended largely on the jury's believing his testimony that Miller had a knife during the fatal confrontation, by undermining his credibility. We need not rule on Carter's self-incrimination claim; for, even assuming the statements were involuntary, we conclude that the error would be harmless beyond a reasonable doubt under Milton v. Wainwright, 407 U.S. 371, 92 S. Ct. 2174, 33 L. Ed. 2d 1 (1972).3

The FBI agent was not the only witness to testify that Carter intended to rely on an alibi. The government produced an inmate who testified that approximately 30 minutes after the assault Carter asked him whether Miller was dead and told him that he was setting up an alibi. Tr. at 67, 68. Another inmate testified that during the five or six days following the incident he and Carter discussed the alibi. Carter told him that he had acted immediately after the attack to create an alibi and that he knew an attorney who would aid and even lie for him. The witness also testified that Carter hoped that Miller's unpopularity with the other inmates would lead them to support his alibi. Tr. at 110-13. A third inmate, who is a physician's assistant, testified that shortly after the incident Carter told him that he had cut his hand on a razor blade imbedded in a bar of soap in the shower. At trial, Carter admitted that he suffered the cut in the scuffle with Miller and went to the physician's assistant as part of his alibi. Even without the FBI agent's testimony, evidence from three other sources disclosed Carter's intention to fabricate an alibi; this untainted evidence also impeached Carter's credibility and undermined his self-defense testimony.

Moreover, when we view the agent's testimony in light of the entire record, as we must, it is clear that the alleged error is harmless. The only evidence of self-defense was Carter's own testimony. He could not corroborate his testimony that Miller had a knife, despite the fact that at least six inmates witnessed the fatal blows. Nor could he corroborate his claim that Miller advanced toward him while he stood his ground; all of the other evidence was that each advanced toward the other or that Carter was the aggressor. Finally, the evidence was uncontradicted that Carter continued to strike Miller with the barbell after Miller had collapsed from the first blow. Even if his credibility had never been attacked, Carter's self-defense testimony would have been inherently suspect: it is self-serving, uncorroborated, and contradicted by overwhelming evidence. On this record, we believe the jury would have found that the government proved beyond a reasonable doubt that Carter did not act in self-defense without relying on the FBI agent's testimony.

In response to defense evidence that Miller was a prison bully who constantly harassed and threatened Carter, the government produced Miller's correctional counselor in rebuttal to testify that Miller was a good prisoner. After the counselor stated that he never received complaints about Miller's conduct, the prosecutor asked whether, in the normal course of business, the counselor would have been informed of any complaints about Miller made to other counselors. The defense objected to the question as calling for hearsay, and the District Court overruled the objection. To the extent that the question and answer contained an implied assertion that no complaints about Miller were made to other counselors, we agree that the question called for hearsay. However, this single error was minuscule in the context of the two-day trial, and it could not have appreciably prejudiced Carter. Therefore we hold that this admission of hearsay evidence is harmless error. Fed.R.Evid. 103(a).

During voir dire, Carter requested the District Court to present three questions to prospective jurors. In substance, the questions asked (1) whether any juror would be reluctant to return a verdict of not guilty if the evidence showed guilt by a preponderance of the evidence, but not beyond a reasonable doubt; and (2) whether any juror would change a vote from not guilty to guilty merely because a majority of jurors voted guilty. The District Court refused to propound these questions, but it thoroughly explained and questioned the panel on the presumption of innocence and the prosecutor's burden of proof beyond a reasonable doubt. The Court also instructed the jurors to exercise independent judgment in evaluating the evidence and to avoid voting for a particular result merely because a majority of jurors supported it. The District Court has broad discretion in propounding voir dire interrogatories, United States v. Spaar, 748 F.2d 1249, 1253 (8th Cir.1984). We cannot say that the Court abused its discretion here. The subjects covered by the requested questions were adequately addressed by the questions actually put by the Court.

The judgment is affirmed.