opinion: Per Curiam.
  Respondent was one of six inmates involved in a 1971 San Quentin Prison escape that resulted in the death of three prisoners and three corrections officers. The State of California jointly tried respondent and five other prisoners on numerous charges, including murder, conspiracy, and assault. The prosecution attempted to show that the Black Panther Party had organized the escape attempt and to link respondent to the conspiracy through his membership in that Party. Respondent’s defense was that state police had organized the breakout and ambushed the escapees to eliminate an important faction of the Black Panther Party.
  During voir dire, the court admonished prospective jurors to reveal their associations, if any, with crimes of violence and their attitudes toward radical groups, including the Black Panthers. Patricia Pagan, who became a juror, testified at voir dire that she had no personal knowledge of violent crimes — as a witness, victim, or otherwise — and that she did not associate the Black Panther Party with any form of violence. However, in the course of the 17-month-long trial, evidence was introduced of a crime, unrelated to those at issue in respondent’s trial, of which juror Pagan had some knowledge. A defense witness identified a Black Panther named Pratt as a police informant involved in the alleged police plot. The prosecution sought to impeach this witness by introducing evidence that Pratt was in custody for the 1968 murder of a Santa Monica woman during the entire period at issue. This evidence triggered juror Fagan’s recollection of the murder of a childhood friend, who was the woman Pratt had been convicted of killing.
  Upon hearing the evidence about Pratt, juror Fagan twice went to the trial judge’s chambers to tell him of her personal acquaintance with Pratt’s 1968 murder victim. She told him that she feared that she might cry if the 1968 murder were explored further at trial. The judge asked her on each occasion whether her disposition of the case would be affected. She assured him that it would not. The judge told her not to be concerned and that the matter probably would not be mentioned again. He made no record of either conversation, and he did not inform the defendants or their counsel about them.
  At the close of trial, the jury found respondent guilty of two counts of murder and of conspiracy to escape, and acquitted him of the remaining charges. The jury also convicted two other defendants of assault, and found insufficient evidence to support the numerous remaining charges. Respondent was sentenced to life imprisonment.
  Counsel for respondent subsequently learned of the ex parte communications between judge and juror and moved for a new trial. At a hearing on the motion, juror Fagan testified that she had not remembered her friend’s death during voir dire and that her subsequent recollection did not affect her ability impartially to judge respondent’s innocence or guilt. She admitted telling other jurors that she personally knew Pratt’s 1968 murder victim, but denied making any disparaging remarks about the Black Panther Party. The trial judge concluded that the ex parte communications “lacked any significance” and that respondent suffered no prejudice therefrom. See App. C to Pet. for Cert. 22. Accordingly, he denied the motion for new trial.
  The California Court of Appeal affirmed the conviction. It found the ex 'parte communication to be federal constitutional error that was harmless' “beyond a reasonable doubt” because the jury’s deliberations, as a whole, were unbiased. Id., at 28-35. The California Supreme Court denied review.
  Respondent then petitioned for a writ of habeas corpus in Federal District Court. The District Court issued the writ, ruling that the ex parte communications between judge and juror violated both respondent’s right to be present during all critical stages of the proceedings and his right to be represented by counsel. 543 F. Supp. 757 (ND Cal. 1982). Furthermore, the District Court held that automatic reversal was necessary because the absence of a contemporaneous record made intelligent application of the harmless-error standard impossible. Alternatively, it concluded that a post-trial hearing could not establish that the constitutional error was harmless beyond a reasonable doubt. Thus, it found that respondent’s conviction had to be vacated because of the state court’s failure to hold a contemporaneous hearing about, or to make a contemporaneous record of, the ex parte communication. The Court of Appeals for the Ninth Circuit affirmed on the basis that an unrecorded ex parte communication between trial judge and juror can never be harmless error. Judgment order reported at 701 F. 2d 186 (1983).
  We emphatically disagree. Our cases recognize that the right to personal presence at all critical stages of the trial and the right to counsel are fundamental rights of each criminal defendant. “At the same time and without detracting from the fundamental importance of [these rights], we have implicitly recognized the necessity for preserving society’s interest in the administration of criminal justice. Cases involving [such constitutional] deprivations are [therefore] subject to the general rule that remedies should be tailored to the injury suffered . . . and should not unnecessarily infringe on competing interests.” United States v. Morrison, 449 U. S. 361, 364 (1981); see also Rogers v. United States, 422 U. S. 35, 38-40 (1975). In this spirit, we have previously noted that the Constitution “does not require a new trial every time a juror has been placed in a potentially compromising situation . . . [because] it is virtually impossible to shield jurors from every contact or influence that might theoretically affect their vote.” Smith v. Phillips, 455 U. S. 209, 217 (1982). There is scarcely a lengthy trial in which one or more jurors do not have occasion to speak to the trial judge about something, whether it relates to a matter of personal comfort or to some aspect of the trial. The lower federal courts’ conclusion that an unrecorded ex parte communication between trial judge and juror can never be harmless error ignores these day-to-day realities of courtroom life and undermines society’s interest in the administration of criminal justice.
  This is not to say that ex parte communications between judge and juror are never of serious concern or that a federal court on habeas may never overturn a conviction for prejudice resulting from such communications. When an ex parte communication relates to some aspect of the trial, the trial judge generally should disclose the communication to counsel for all parties. The prejudicial effect of a failure to do so, however, can normally be determined by a post-trial hearing. The adequacy of any remedy is determined solely by its ability to mitigate constitutional error, if any, that has occurred. See, e. g., United States v. Morrison, supra, at 365; Rogers v. United States, supra, at 40. Post-trial hearings are adequately tailored to this task. See, e. g., Smith v. Phillips, supra, at 218-219, and n. 8; Remmer v. United States, 347 U. S. 227, 230 (1954).
  The final decision whether the alleged constitutional error was harmless is one of federal law. Chapman v. California, 386 U. S. 18, 20-21 (1967). Nevertheless, the factual findings arising out of the state courts’ post-trial hearings are entitled to a presumption of correctness. See 28 U. S. C. § 2254(d); Sumner v. Mata, 449 U. S. 539 (1981). The substance of the ex parte communications and their effect on juror impartiality are questions of historical fact entitled to this presumption. Thus, they must be determined, in the first instance, by state courts and deferred to, in the absence of “convincing evidence” to the contrary, by the federal courts. See Marshall v. Lonberger, 459 U. S. 422, 431-432 (1983). Here, both the State’s trial and appellate courts concluded that the jury's deliberations, as a whole, were not biased. This finding of “fact” — on a question the state courts were in a far better position than the federal courts to answer — deserves a “high measure of deference,” Sumner v. Mata, 455 U. S. 591, 598 (1982), and may be set aside only if it “lack[s] even ‘fair support’ in the record.” Marshall v. Lonberger, 459 U. S., at 432. The absence of a contemporaneous recording will rarely deprive the finding of “even ‘fai[r] suppor[t]’ in the record.” See ibid.
  The post-trial hearing in this ease created more than adequate support for the conclusion that juror Fagan’s presence on the jury did not prejudice respondent. The 1968 murder was not related to the crimes at issue in the trial. Pratt was not connected to any of the offenses for which respondent was convicted, and he did not testify at the trial. Juror Fagan never willfully concealed her association with the Santa Monica crime, and she repeatedly testified that, upon recollection, the incident did not affect her impartiality. She turned to the most natural source of information — the trial judge — to disclose the information she should have recalled but failed to recall during voir dire. Their ex parte communication was innocuous. They did not discuss any fact in controversy or any law applicable to the case. The judge simply assured her that there was no cause for concern. Thus, the state courts had convincing evidence that the jury’s deliberations, as a whole, were not biased by the undisclosed communication of juror Fagan’s recollection. The lower federal courts should have deferred to this presumptively correct state-court finding and therefore should have found the alleged constitutional error harmless beyond a reasonable doubt.
  Accordingly, we grant the motion of respondent for leave to proceed informa pauperis and the petition for certiorari, vacate the judgment of the Court of Appeals, and remand the case for further proceedings consistent with this opinion.
  It is so ordered.
  Justice Brennan dissents from this summary disposition. He would grant the petition for certiorari and set the case for oral argument.
  Respondent also argued that his due process right to be presumed innocent was violated when he was forced to stand trial shackled and chained. Neither the District Court nor the Court of Appeals reached this issue. Given our disposition of the case, this issue only remains to be resolved on remand.
  Petitioners have apparently conceded, in both federal and state court, that the undisclosed ex parte communications established federal constitutional error. See Pet. for Cert. 29-31. We acknowledge that the trial judge promptly should have notified counsel for all parties after the juror approached him. Whether the error was of constitutional dimension in this case is not before us. Because we find that no actual prejudice was shown, we assume, without deciding, that respondent’s constitutional rights to presence and counsel were implicated in the circumstances of this case.
  Justice Stevens suggests that the only constitutional right implicated in this case is a possible due process right to a midtrial hearing on the subject of the juror’s impartiality. See post, at 126 (Stevens, J., concurring in judgment). Had the State raised the underlying constitutional right as an issue in the courts below and in the petition for certiorari, this approach might merit consideration. But the case came to us alleging harmless violations of the right to be present during all critical stages of the proceedings and the right to be represented by counsel, and we therefore analyze only that challenge. These rights, as with most constitutional rights, are subject to harmless-error analysis, see, e. g., United States v. Morrison, 449 U. S. 361, 364-365 (1981) (right to counsel); Snyder v. Massachusetts, 291 U. S. 97, 114-118 (1934) (right to presence), unless the deprivation, by its very nature, cannot be harmless. See, e. g., Gideon v. Wainright, 372 U. S. 335 (1963).
  Thus, we have refused, on facts more troublesome than these, to find inherent bias in a verdict when a state trial court determined “beyond a reasonable doubt” that a juror’s out-of-court action did not influence the verdict. In Smith v. Phillips, 455 U. S. 209 (1982), a criminal defendant contended that he had been denied due process because, during his state-court trial, one of the jurors applied to the prosecutor’s office for a job as an investigator. The application was not brought to the parties’ attention until sometime after the verdict was rendered. The state court held a post-trial hearing and, relying on the juror’s own testimony, found “beyond a reasonable doubt” that the juror’s action had not influenced the verdict. We concluded that, in the circumstances of that case, it would not be proper to impute bias in the verdict or to find a post-trial hearing inadequate as a remedy for the alleged due process violation. Id., at 219. The facts here involve no inference of juror misconduct or third-party influence, and therefore are of far less concern than the conduct at issue in Smith. See infra, at 120-121. Thus, a post-trial hearing is adequate to discover whether respondent was prejudiced by the undisclosed communications about juror Fagan’s recollection.
  See, e. g., Rogers v. United States, 422 U. S. 35, 38-40 (1975) (although violation of Federal Rule of Criminal Procedure 43 may be harmless error, additional instructions from judge to jury, without notification to defendant or his counsel, is not); Shields v. United States, 273 U. S. 583, 588-589 (1927) (undisclosed instructions from judge' to jury violate non-constitutionally based rules of orderly trial procedure); Fillippon v. Albion Vein Slate Co., 250 U. S. 76, 81 (1919) (same).
  A juror may testify concerning any mental bias in matters unrelated to the specific issues that the juror was called upon to decide and whether extraneous prejudicial information was improperly brought to the juror’s attention. See Fed. Rule Evid. 606(b); Smith v. Phillips, supra, at 217, and n. 7, 218-219, and n. 8. But a juror generally cannot testify about the mental process by which the verdict was arrived. See Mattox v. United States, 146 U. S. 140 (1892). Thus, the California Court of Appeal refused to consider certain testimony in arriving at its decision that respondent had not suffered prejudice “beyond a reasonable doubt.” App. C.to Pet. for Cert. 33. The District Court improperly refused to defer to the California Court of Appeal’s sensitive review of this evidence. See 543 F. Supp. 757, 773-774 (ND Cal. 1982).
  Although Justice MARSHALL’S dissent purportedly agrees that the District Court was obliged to defer to the California Court of Appeal’s finding that the jury’s deliberations were not biased if that finding had “even ‘fair support’ in the record,” post, at 143, its critique of the circumstances underlying that finding proves otherwise. The dissent concedes, albeit grudgingly, that each circumstance the California Court of Appeal relied on in concluding “beyond a reasonable doubt” that the jury’s impartiality was not impaired was probative. See post, at 143-148. But the dissent, like the District Court below, argues that each circumstance is defective either because it depends on the juror’s own statements concerning her impartiality or because “the potential for impairment of the jury’s impartiality [in each] was considerable.” See post, at 148. Thus, the dissent, like the District Court, bases its conclusion not on a “lack of even fair support in the record” but on its own evaluation of the credibility of the witnesses, see, e. g., post, at 145, n. 29, and a concern about the potential for prejudice in the underlying circumstances.
  Such an approach plainly fails to adhere to the commands of the applicable statute. Title 28 U. S. C. § 2254(d) provides that the state courts’ determinations about witness credibility and inferences to be drawn from the testimony were binding on the District Court and are binding on us. See Marshall v. Lonberger, 459 U. S. 422, 434 (1983). Title 28 U. S. C. § 2254(d) requires that a federal habeas court more than simply disagree with the state court before rejecting its factual determinations. It must conclude that the findings “lac[k] even ‘fair support’ in the record.” 459 U. S., at 432. That statutory test is satisfied by the existence of probative evidence underlying the California Court of Appeal’s conclusion that the jury’s impartiality was unimpaired “beyond a reasonable doubt.” Ibid. Thus, our holding necessarily follows from the state courts’ findings of fact and from the presumption of correctness accorded to those findings.
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