J. JOSEPH SMITH, Circuit Judge:

This is an appeal from a judgment of the United States District Court for the Southern District of New York, Thomas P. Griesa, Judge, denying the petition for writ of habeas corpus of Jose Luis Sullivan, impris *466 oned after conviction on murder and weapons counts in the Supreme Court of the State of New York, Bronx County. We reverse and remand for further proceedings.

The appellant, Jose Luis Sullivan, was convicted in 1973 after a jury trial in New York Supreme Court, of two counts of murder and one count of illegal possession of a weapon. About one month after trial, a juror, Joseph Villanacci, complained to the Bronx District Attorney of harassment by “voices.” Villanacci was brought before the trial court for questioning to determine whether he was competent during trial. Villanacci’s testimony at this hearing seemed to indicate that he had been experiencing delusions or paranoid sensations during the trial. He said that he heard “vibrations” throughout the trial and that the vibrations were particularly intense in the jury room. He stated that “through these sounds I heard the voice, I heard my name” and “they were spying, they were spying maybe in favor of the defendant.” He also stated that he had heard voices once before, while on jury duty in 1969 at a criminal trial resulting in conviction. Villanacci said that the voices had not influenced him in his verdict, and had not communicated anything unfavorable about the defendant, the witnesses or the attorneys.

The trial judge appointed a psychiatrist, Dr. Lubin, to examine Villanacci. Dr. Lu-bin examined Villanacci independently and made a written report to the court, which was incorporated into the record at the time of sentencing. Dr. Lubin’s report stated that Villanacci had heard voices during trial telling him to “vote for the defendant” and that defendant was “not a murderer.” It stated that “patient explained that he followed his logical judgment and voted ‘guilty.’ ” Dr. Lubin’s impression was that Villanacci had a “schizoid personality with paranoid features . . . vulnerable to a paranoid psychotic decompensation.” However, Dr. Lubin concluded that Villanacci had been a competent juror:

He heard the voices but they did not influence him and his logic in evaluating the factors in the trial and coming to the conclusion that he did was quite sound. Although he heard the voices, he had not formulated them into a systematized delusion; i. e., he did not, in fact, come to a definite conclusion as to who his persecutors might be ... . [H]e was competent to make a rational judgment on the merits of the case presented to him in the court.

The defendant had no opportunity to present the testimony of his own psychiatrist or to cross-examine Dr. Lubin about his conclusion. The court incorporated Dr. Lubin’s written statement into the record and concluded that there was “no necessity for further inquiry, especially in view of the very clear statement made by Dr. Lubin by way of report to this court. . . . ”

The conviction was affirmed by the New York Supreme Court, Appellate Division, and the New York Court of Appeals; defendant’s objection to the determination of competence was raised on appeal and rejected. Two judges in the Appellate Division panel dissented on various grounds, including the failure to afford defendant an opportunity to have his own psychiatrist examine Villanacci and to cross-examine Dr. Lubin. Sullivan applied for a writ of habeas corpus in federal district court, which was denied. The court stated:

In the absence of an independent adjudication of incompetency of the juror in question close to the time of jury service, there is no occasion for disturbing a jury verdict because of a question of mental capacity. Moreover, there is no occasion to hold a hearing on the matter. United States v. Dioguardi, 492 F.2d 70, 80 (2d Cir. 1974), cert. denied, 419 U.S. 829 [95 S.Ct. 49, 42 L.Ed.2d 53] (1975).

Sullivan contends on appeal that he was denied due process when the trial court failed to conduct a “full and fair hearing” on the issue of juror competence. He contends that although it might have been proper not to grant any hearing at all, once a further inquiry was ordered, the defendant should at least have been allowed to present his own witness and conduct a cross-examination.

*467 Due process requires that jurors be sane and competent during trial. Peters v. Kiff, 407 U.S. 493, 501, 509, 92 S.Ct. 2163, 33 L.Ed.2d 83 (1972); Jordan v. Massachusetts, 225 U.S. 167, 32 S.Ct. 651, 56 L.Ed. 1038 (1912). Once a preliminary showing of incompetence or juror misconduct has been made there is a corresponding right to an inquiry into the relevant surrounding circumstances. Remmer v. United States, 347 U.S. 227, 74 S.Ct. 450, 98 L.Ed. 654 (1954) (“Remmer P’); see also United States ex rel. Owen v. McMann, 435 F.2d 813 (2d Cir. 1970), cert. denied, 402 U.S. 906, 91 S.Ct. 1373, 28 L.Ed.2d 646 (1971). The questions involved here are: (1) How strong a preliminary showing must defendant make in order to trigger a hearing into juror competence? and (2) Once a sufficient showing is made, what sort of hearing is required?

Improper external influences such as jury tampering are presumptively prejudicial. Remmer I, supra, 374 U.S. at 229, 74 S.Ct. 450. 1 A showing of “reasonable grounds” to believe that there has been tampering will trigger a post-verdict exploration of the “entire picture.” Remmer v. United States, 350 U.S. 377, 379, 76 S.Ct. 425, 100 L.Ed. 435 (1956) (“Remmer II’); United States v. Moten, 582 F.2d 654, 664 (2d Cir. 1978). Where the allegations involve considerations internal to the jury deliberation process, such as juror insanity, this court has required “strong evidence that it is likely that the juror suffered from such incompetence” before ordering a post-verdict inquiry. United States v. Dioguardi, 492 F.2d 70, 78 (2d Cir. 1974). This high threshold is intended to avoid post-verdict harassment of jurors, preserve the finality of judgments, discourage meritless applications for post-verdict hearings, and reduce the likelihood of and temptation for jury tampering. McDonald v. Pless, 238 U.S. 264, 267-268, 35 S.Ct. 783, 59 L.Ed. 1300 (1915); Mattox v. United States, 146 U.S. 140, 148-149, 13 S.Ct. 50, 36 L.Ed. 917 (1892); United States v. Crosby, 294 F.2d 928, 950 (2d Cir. 1961), cert. denied sub nom. Mittelman v. United States, 368 U.S. 984, 82 S.Ct. 599, 7 L.Ed.2d 523 (1962).

Here there was a sufficient showing of incompetence to justify, indeed to require, a further inquiry by the trial court. The unsolicited statements of the juror himself were strongly suggestive of incompetence during trial and deliberations. Although Villanacci stated that he was not influenced by the voices he heard, this statement should be discounted in light of the evidence of psychological instability which also emerged from Villanacci’s statements. Moreover, a juror’s statement that he remained impartial in the face of a potentially prejudicial influence is not conclusive. See Irvin v. Dowd, 366 U.S. 717, 81 S.Ct. 1639, 6 L.Ed.2d 751 (1961). United States v. Dioguardi, supra, is distinguishable. In Dioguardi, unlike this case, there was no evidence that the alleged feelings of clairvoyance and other psychic phenomena exhibited by the juror after trial were present during trial. In addition, the evidence in that case consisted of a letter written by the juror to the defendant. Here the juror’s own statements indicated that the delusions occurred during trial, and there was ample justification for ordering a further inquiry.

We also find that, given that a hearing was required, it was not sufficient for *468 the judge to obtain the written report of a psychiatrist, with nothing more. Sullivan should have been allowed to cross-examine Dr. Lubin about his conclusions regarding Villanacci’s competence. The trial court has some discretion to determine the form of the hearing. United States v. Boscia, 573 F.2d 827, 831 (3rd Cir.), cert. denied, 436 U.S. 911, 98 S.Ct. 2248, 56 L.Ed.2d 411 reh. denied, 438 U.S. 908, 98 S.Ct. 3130, 57 L.Ed.2d 1152 (1978); Tillman v. United States, 406 F.2d 930, 938 (5th Cir. 1969); United States v. Miller, 381 F.2d 529, 539 (2d Cir. 1967); United States v. Flynn, 216 F.2d 354, 372 (2d Cir. 1954). Given the clear due process right to a sane and competent jury, however, such hearings may not completely ignore due process safeguards which are designed to promote thorough and accurate factfinding. If the post-verdict hearing is to be restricted, the restrictions must take into account the policies which underlie the reluctance to hold such hearings. See McDonald v. Pless, supra, 283 U.S. at 267-268, 35 S.Ct. 783. None of these policies militates against relief here. Finality of judgment is affected by any post-verdict inquiry; it is not specific to the problem here. Cross-examination of the psychiatrist in this case would not have increased and will not in any way increase the amount of juror harassment. The opportunity for tampering will not be enhanced.

The juror willingly submitted to Dr. Lu-bin’s examination. An opportunity for cross-examination of Dr. Lubin will not at this time further concern Villanacci. On the other hand, another psychiatric examination of the juror at- this late date would be of little, if any, value and would significantly increase the harassment.

Here there is a finding of serious mental illness coupled with an opinion that the juror was at the same time still competent to act on the case. Some opportunity to test by cross-examination the basis of the opinion in the light of the finding cannot fairly be denied. In light of the serious question as to the juror’s competence, we think that due process requires at least the opportunity to test Dr. Lubin’s opinion on cross-examination.

The judgment is reversed and the case remanded to the district court with instructions to grant the writ unless the state, within 60 days or such further time as may be fixed by the district court, reopens the hearing and provides an opportunity for cross-examination of Dr. Lubin or grants Sullivan a new trial.

Notes

. Remmer I involved allegations that an attempt had been made to bribe a juror. The Court stated that:

[t]he trial court should not decide and take final action ex parte on information such as was received in this case, but should determine the circumstances, the impact thereof upon the juror, and whether or not it was prejudicial, in a hearing with all interested parties permitted to participate.

Remmer v. United States, 347 U.S. 227, 229-230, 74 S.Ct. 450, 451, 98 L.Ed. 654 (1954). On remand, the district court held a hearing and found that the incident had been harmless. In Remmer v. United States, 350 U.S. 377, 76 S.Ct. 425, 100 L.Ed. 435 (1956) (“Remmer II”), the Court granted a new trial, stating that the hearing below had been too narrow in scope, and that “[i]t was the paucity of information relating to the entire situation coupled with the presumption which attaches to the kind of facts alleged by petitioner which, in our view, made manifest the need for a full hearing.” 350 U.S. at 379-380, 76 S.Ct. at 427 (emphasis added).