FLAUM, Circuit Judge.
Randall Weidner, a state prisoner, seeks a writ of habeas corpus based on the admission at his criminal trial of what he claims was an involuntary confession. In a prior opinion, this Court remanded Weid-ner’s petition to the district court with instructions relating to the gathering of evidence concerning the state trial court’s ruling that Weidner’s confession was voluntary. After complying with these instructions, the district court again denied Weid-ner’s petition. Because our prior instructions are the law of the case, and because none of the exceptions to the law of the case doctrine are applicable, we affirm the district court’s decision to deny the petition.
I. FACTS AND PRIOR PROCEEDINGS
In August 1979, Randall Weidner was arrested in Calumet City, Illinois on suspicion that he had committed a rape and murder a few days earlier. At the time of his arrest, Weidner was seventeen, had an eighth-grade education, and was a frequent user of hallucinogenic drugs. City police took him to the stationhouse and began to interrogate him; within an hour he eonfess-ed to both crimes. At trial in 1981 he moved unsuccessfully to suppress his statement. In denying Weidner’s motion, the state judge neglected to make subsidiary factual findings concerning whether Weid-ner had, as he claimed, been threatened or coerced by the police officers who questioned him. Based in part on the admission of the statements he made to the police, Weidner was convicted of rape, conspiracy to murder, and murder, and was sentenced to 80 years in prison. Weidner’s conviction was affirmed on appeal.
People v. Visnack,
135 Ill.App.3d 113, 89 Ill.Dec. 901, 481 N.E.2d 744 (1st Dist.1985). The Illinois Supreme Court denied review.
In 1987, Weidner petitioned the district court for a writ of habeas corpus. The district court denied his petition.
Weidner v. Thieret,
683 F.Supp. 1195 (N.D.Ill.1988). It found that there was no evidence that the state trial court had applied incorrect principles of law in reaching its decision that Weidner’s incriminating statements were voluntary. Implicit in the state judge’s denial of Weidner’s motion to suppress, the district court concluded, were two factual findings: first, that the testimony of the two officers who interrogated Weidner that they had not threatened or coerced him into confessing was credible, and second, that Weidner’s testimony that he had been coerced or threatened was not.
Id.
at 1198-99. The district court held that these implicit findings qualified for the presumption of correctness afforded state factual findings in federal habeas proceedings,
see
28 U.S.C. § 2254(d), and denied Weid-ner’s request for a de novo evidentiary hearing to determine whether his confession was voluntary.
Id.
at 1198.
Weidner appealed the district court’s denial of his petition to this Court. While recognizing that “[a] state trial judge is not required to make detailed findings of fact in deciding that a confession is admissible,”
Weidner v. Thieret,
866 F.2d 958, 963 (7th Cir.1989) (hereinafter,
“Weidner
I”), we
nevertheless decided that the state court’s ruling provided insufficient information as to “the facts underlying Weidner’s confession.”
Id.
Because the state court’s sparse factual findings failed to elucidate these facts, we reversed the district court’s holding that Weidner’s petition could be dismissed without a hearing.
To guide the district court on remand, we suggested two procedures it could follow to uncover more information about the basis for the state court’s ruling. The first called for the state to “submit an affidavit from the state trial judge explaining his cryptic and ambiguous ruling.”
Id.
The second was for the district judge to invite Weidner and the police officers who questioned him “to testify about what went on during the interrogation,” allowing the district judge to “make his own findings of fact.”
Id.
Neither of these procedures required in-court testimony from the state judge, reflecting our discomfort at the prospect of a federal district court calling as a witness at a habeas hearing a state judge who would be asked “to give testimony and be cross-examined with respect to implicit findings that he may have made many years earlier.”
Id.
On remand to the district court, the state opted for the first of the two alternative procedures we proposed and presented an affidavit from the state trial judge. In the judge’s first affidavit, he stated that he had an independent recollection of Weid-ner’s case, but had also looked at the transcript of the 1981 suppression hearing. He explained that he denied Weidner’s motion to suppress because he believed the testimony of the police officers who questioned Weidner, but did not believe the testimony of Weidner or the psychiatrist who testified on his behalf. As to the psychiatrist, the state judge stated that his testimony was deficient because his examination of Weid-ner was brief, occurred nearly a year after the police questioning, and was at odds with credible police testimony that at the time of his interrogation Weidner appeared to them to have the mental capacity to waive his rights knowingly and intelligently.
Weidner moved to strike the state judge’s initial affidavit. Rather than granting the motion, the district court chose to allow the state judge to submit a supplemental affidavit which addressed more fully the specific coercive acts that Weidner alleged had occurred during the course of his interrogation. The state judge availed himself of this opportunity, submitting a much longer and more detailed affidavit.
In this affidavit, the state judge gave reasons why he was able to independently recall Weidner’s trial from among the numerous felony trials he had presided over during his years on the bench and identified the steps he took to refresh his recollection with respect to the voluntariness issue that was the focus of the habeas proceeding. He specifically rejected Weid-ner’s allegations that a police investigator had played with his weapon or pointed it at Weidner during the interview, that the investigator had physically harmed Weidner, or that the investigator had used abusive language toward Weidner. Turning to the conduct of the other interviewing officer, the state judge similarly rejected Weidner’s charges that this officer had threatened him with a weapon, told him that he would die in the electric chair, or would feel better if he talked. The state judge also stated that neither the two interrogating officers nor the assistant state’s attorney who transcribed Weidner’s incriminating statement ever denied Weidner access to a phone to call his parents. “In summary,” he wrote, “no force, threats, coercion, promises, misrepresentations, or any other improper means had been used to secure a statement from Weidner, and [ ] Weidner’s statements were voluntary.” Supplemental Affidavit at 7. As to
Miranda
warnings, the state judge found that Weidner had been read his rights at the scene of his arrest, at the station house prior to his interrogation by the two police officers, and by the assistant state’s attorney before he transcribed Weidner’s confession. Weidner, he wrote, “was capable of understanding such rights and did knowingly and intentionally waive them.”
Id.
In response to the state trial judge’s supplemental affidavit, Weidner renewed his motion to strike, and moved in the alternative that the state judge be required to present his evidence (and subject himself to cross-examination) in open court or in a videotaped deposition. In support of this motion, Weidner filed the affidavit of Lyn and Ralph Haber, professors of psychology and experts in cognition. The Habers took the view that the affidavit procedure suggested by this Court in
Weidner I
“far exceeds any reasonable expectation of satisfactory compliance, based on what is known about the nature and capacity of human memory.” Haber Affidavit at ¶ 17. The Habers argued that principles of cognitive psychology indicated that the state judge’s recollection of the mental processes that led up to his ruling that Weidner’s confession was voluntary had inevitably become clouded through the passage of time and the numerous similar rulings he had made, and was likely to be biased by the judge’s interest in seeing his previous decision vindicated on collateral review.
The district court, unpersuaded by the Habers’ affidavit, once again denied Weid-ner’s petition. It also examined the alternative ways of obtaining information concerning the events leading up to the confession that Weidner proposed: first, a hearing at which the state judge would give testimony, second, a videotaped deposition, and third, an evidentiary hearing at which both Weidner and the officers who interrogated him — but not the state judge — would testify. As to the first and second alternatives, the district court observed that both were contrary to the sensitivity this Court expressed in
Weidner I
concerning compelling state judges to testify in federal habe-as proceedings. As to the evidentiary hearing, the district court disagreed with Weidner’s suggestion that, because the principles of cognition presented by the Habers suggested that the state judge’s testimony was unreliable, his affidavit should be stricken. The district court observed that all affidavits are subject to attack on the ground that the affiant may not remember the events about which she writes, and accepting Weidner’s memory-loss argument would require a hearing to test the memory of every affiant, nullifying the use of affidavits in judicial proceedings.
II. LAW OF THE CASE
The district court concluded its opinion on remand by noting that the affidavit procedure was one of two this Court in
Weid-ner I
suggested were “acceptable means of clarifying [the state judge’s] factual findings.” It characterized Weidner’s argument that the affidavit procedure was unreliable as “nothing more than an attempt to evade the mandate of the Seventh Circuit.” 735 F.Supp. 284, at 286. Weid-ner renews that attempt on appeal, arguing that our recommendation to the district court in
Weidner I
that it receive evidence from the state court trial judge in the form of an affidavit “violates the habeas corpus statute, is inconsistent with prior decisions of the Supreme Court, and ignores relevant psychological research findings.” Brief at 18. Respondents reply that we are precluded from considering Weidner’s challenges to the affidavit procedure by the doctrine of “law of the case.”
Weidner recognizes that the doctrine of “law of the case” would ordinarily preclude our reconsideration of the affidavit procedure we recommended to the district court in our prior decision. Brief at 19;
see Indianapolis Power & Light v. NLRB,
898 F.2d 524, 528 (7th Cir.1990);
Parts & Elec. Motors v. Sterling Elec.,
866 F.2d 228, 231 (7th Cir.1988),
cert. denied,
— U.S. -, 110 S.Ct. 141, 107 L.Ed.2d 100 (1989). Nevertheless, he contends that we are free to reconsider the affidavit procedure because this appeal falls within one or more exceptions to that doctrine.
The first exception Weidner points us to is applicable where, on remand after the first appeal, new evidence has emerged that differs substantially from than that heard in the trial prior to the first appeal. Brief at 21;
see Evans v. City of Chicago,
873 F.2d 1007, 1014 (7th Cir.1989),
cert. denied,
— U.S. -, 110 S.Ct. 2560, 109 L.Ed.2d 742 (1990);
Barrington Press v. Morey,
816 F.2d 341, 342-43 n. 2 (7th Cir.),
cert. denied, 484 U.S. 906, 108 S.Ct. 249, 98 L.Ed.2d 207 (1987). The second exception Weidner seeks to have us apply comes into play when the prior appellate decision "`was clearly erroneous and would work a substantial injustice.'" Evans, 873 F.2d at 1015.
A. The New Evidence Exception
The doctrine of law of the case reflects the "`sound policy that, when an issue is once litigated and decided, that should be the end of the matter.'" Indianapolis Power & Light, 898 F.2d at 529 (quoting Evans, 873 F.2d at 1014); see Rothner v. City of Chicago, 929 F.2d 297, 301-02 (7th Cir.1991). This "sound policy" would be easily circumvented if any new evidence introduced on remand could serve as a basis for escaping the force of the doctrine. This suggests that for an appellate court to reconsider its past decision, the evidence on remand must not only be different from the evidence presented in the initial trial, but so different and so central to the decision of the case as to leave the second appellate panel with "substantial doubt as to the correctness" of the prior decision. Evans, 873 F.2d at 1014. We cannot say that the Habers' informed doubts that the information contained in the state trial judge's affidavit would be accurate and unbiased meets this standard.
We reach this conclusion because we agree with the district court's view that the Haber affidavit proves too much. As the district court observed in its opinion on remand, accepting the Habers' premise would subject every affidavit filed in the course of litigation to challenge on the ground that the affiant's recall was suspect. More generally, the Habers' affidavit casts doubt not only upon the reliability of the state judge's recollection, but also upon the utility of the alternate procedure Weidner would have us require the district court to use, an evidentiary hearing at which he and his interrogators would testify about the circumstances that led to his confession. Some of the Habers' discussion relates specifically to judges, but the great majority applies to human memory in general. Simply put, the arguments the Habers make concerning the reliability of the state judge's affidavit are equally applicable to the testimony of the police officers who interrogated Weidner, the assistant state's attorney who transcribed his confession, and Weidner himself.
Weidner argues that, unlike the affidavit process we suggested in Weidner I, an evidentiary hearing would subject all witnesses to cross-examination. If the Ha-bers' affidavit correctly assesses the capacity of human memory, however, this hearing is unlikely to provide reliable testimony concerning what occurred in the course of Weidner's interrogation. As to the bias that the Habers argue infects the state trial judge's affidavit, he is not the only one with an interest in the outcome of the hearing Weidner seeks. The state judge has only his reputation to protect. If Weid-ner's story is true, his police interrogators and the state's attorney have a greater incentive to hide their past misdeeds. Weidner himself, of course, has the strongest interest of all in having the hearing come out his way. The Habers' affidavit prefigures a hearing at which all the witnesses are unable to remember, or are too biased to relate accurately, the circumstances leading up to Weidner's confession.
In a sense then, the Habers' affidavit does call into question the affidavit procedure. It also calls into question the utility of all other procedures convened in a habe-as case for the purpose of uncovering "material facts ... not adequately developed at the State court hearing," 28 U.S.C. § 2254(d)(3), or reconciling factual disputes "not resolved in the State court hearing," id., § 2254(d)(1).
However, because the
Habers' criticism is equally applicable to both the affidavit process we recommended in our prior opinion and the hearing he seeks, its effect on this case, where the alternatives posed by Weidner are the state judge's affidavit or a hearing (live or videotaped), favors neither Weidner nor the state. The narrow "new evidence" exception to the doctrine of the law of the case requires that the new evidence developed on remand cast more doubt upon the correctness of our prior ruling.
B. The Clearly Erroneous Exception
The second exception to the doctrine of law of the case that Weidner asks us to apply in this case arises when the prior decision "`was clearly erroneous, and would work a substantial injustice.'" Indianapolis Power & Light, 898 F.2d at 529 (quoting Evans, 873 F.2d at 1014). As in other contexts, the import of the phrase "clearly erroneous" here is that we can only find that a prior decision is not law of the case if "`on the entire evidence, [we] are left with the definite and firm conviction that a mistake has been committed.'" Anderson v. Bessemer City, 470 U.S. 564, 573, 105 S.Ct. 1504, 1511, 84 L.Ed.2d 518 (1985) (quoting United States v. United States Gypsum Co., 333 U.s. 364, 395, 68 5.Ct. 525, 542, 92 L.Ed. 746 (1948)); see Rothner, supra, 929 F.2d at 801 & n. 6. The "clearly erroneous" exception is narrow not just because of the efficiency and finality concerns that animate the law of the case doctrine in general, but also because every decision that a prior appellate opinion is clearly erroneous marks a departure from principles of stare decisis.
The exception, moreover, requires not just that we conclude that a prior decision was "clearly erroneous" but also that it "would work a substantial injustice." In a habeas case, "substantial injustice" obviously includes the continued detention of an innocent petitioner; it is less apparent that it includes other errors that do not raise doubts about the correctness of the outcome reached at the state trial or the denial of the petition by the district court. See 1 J. Liebman, Federal Habeas Corpus Practice and Procedure § 2.2(c) (1988 & Supp.1989) (reviewing debate on relevance of guilt in habeas corpus proceedings); cf. Kuhlmann v. Wilson, 477 U.S. 436, 454, 106 S.Ct. 2616, 2627, 91 L.Ed.2d 364 (1986) (successive federal habeas review available only where the prisonercan make showing that "he has a colorable claim of factual innocence.").
In this case, we cannot say that the affidavit procedure we recommended in Weidner I was clearly erroneous or worked a substantial injustice. Weidner's legal theory is that obtaining an affidavit from a state judge concerning the judge's mental processes violates the habeas statute. According to Weidner, whenever state judges fail to make factual findings of the kind that merit the presumption of correctness afforded by the federal habeas statute, see 28 U.S.C. § 2254(d), the federal habeas court must hold a hearing to enable it to determine the relevant facts de novo.
We agree that when a state court has made no explicit or implicit factual findings, or when these findings are inadequate, some kind of hearing is necessary to resolve the facts upon which the outcomes of habeas proceedings so frequently turn. This is the command of the Supreme Court's decision in Townsend v. Sain, 372 U.S. 293, 314, 83 S.Ct. 745, 757-58, 9 L.Ed.2d 770 (1963), upon which § 2254(d) was patterned. See Miller v. Fenton, 474 U.S. 104, 115, 106 S.Ct. 445, 452, 88 L.Ed.2d 405 (1985). The more difficult question is whether we clearly erred in Weidner I when we concluded that the hearing we instructed the district court to hold could begin and end with "an affidavit from the state trial judge explaining his cryptic and ambiguous ruling," Weidner I, 866 F.2d at 963, that Weidner's confession was voluntary.
The habeas corpus statute itself suggests that we did not. Congress has expressly provided for the admissibility in habeas hearings of “the certificate of the judge who presided at the trial resulting in the judgment, setting forth the facts occurring at the trial.” 28 U.S.C. § 2245. Though used infrequently, § 2245 certifications have in the past proven useful to district courts seeking to uncover the facts surrounding state criminal prosecutions when the outcome of these prosecutions are challenged on collateral review.
See, e.g., Bassette v. Thompson,
915 F.2d 932, 939 (4th Cir.1990);
Gray v. Estelle,
574 F.2d 209 (5th Cir.1978). These certifications have at times involved inquiries into the mental processes of state trial court judges, implying an interpretation of the phrase “facts occurring at trial” that is broader than purely historical facts and includes the trial judge’s state of mind with respect to a particular issue at a particular time at trial.
See, e.g., Bassette,
915 F.2d at 938 (state trial judge’s certification that defendant’s refusal to accept responsibility for murder during pre-sentencing interview in capital case did not influence his recommendation that defendant be sentenced to death). Federal courts reviewing habeas petitions have scrutinized these certifications to see if they are at odds with the record of the state trial,
see Wang v. Withworth,
811 F.2d 952, 957 (6th Cir.),
cert. denied,
481 U.S. 1051, 107 S.Ct. 2185, 95 L.Ed.2d 842 (1987), or sufficiently unequivocal,
see Strader v. Troy,
571 F.2d 1263, 1267 (4th Cir.1978).
It is true, as Weidner reminds us, that some courts have expressed doubt as to the value of testimony from judges, either in habeas proceedings or more generally. In
Washington v. Strickland,
693 F.2d 1243, 1262-63 (5th Cir. Unit B 1982)
(en banc), rev’d on other grounds,
466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), the state trial judge testified in the district court concerning his reasons for imposing the death penalty on the habeas petitioner. In considering the admissibility of this evidence, the appeals court drew a distinction between judicial testimony concerning “personal knowledge of historical facts,” which it ruled was admissible, and testimony in which the state judge had “explained his reasons for imposing the death sentence and his probable response to evidence adduced at the habeas hearing,”- which it ruled was not.
Strickland,
693 F.2d at 1263;
see also Morrison v. Kimmelman,
650 F.Supp. 801, 805-07 (D.N.J.1986). The
Strickland
court identified several reasons underlying its conclusion that judicial testimony concerning mental processes was inadmissible. The first was the “special risks of inaccuracy” such testimony poses because of the lapse of time. 693 F.2d at 1263. The second was the threat this testimony posed to the “finality and integrity of judgments.”
Id.
The third was the tension between federal and state courts that “a rule that allows the probing of the mental processes of a state judge” at habeas hearings creates.
Id.
While we are sympathetic to the concerns raised by the use of judicial testimony, they do not convince us that the procedure outlined in our earlier opinion was clearly erroneous. First, none of the three reasons given in the
Strickland
opinion supports the distinction the opinion draws between testimony concerning historical facts and testimony concerning mental processes. Memories of mental processes are not, to our knowledge, more perishable than memories of historical facts. Both potentially pose the same threat to the finality of a judgment, as finality may be called into question equally by a judge’s memory of what happened at a particular moment at trial and a judge’s memory of why she ruled a certain way on a particular motion. As to the comity concerns implicated by calling state court judges to testify in federal habeas proceedings, these apply equally no matter what, the state judge is questioned about.
One reason for distinguishing testimony concerning mental processes from testimony about historical facts is the concern that the former is essentially irrebuttable, while the latter may not be.
See Fayerweather v. Ritch,
195 U.S. 276, 307, 25 S.Ct. 58, 67-68, 49 L.Ed. 193 (1904) (“[N]o testimony should be received except of open and
tangible facts — matters which are susceptible of evidence on both sides.”)- Past courts hearing habeas cases, however, have accepted § 2245 certifications relating to the mental processes of state court judges.
See, e.g., Bassette,
915 F.2d at 932.
Moreover, this case implicates none of the three concerns identified in the
Strickland
opinion. We are cognizant of the danger of memory loss, but as we discuss above,
see supra
at 630, fading recollections pose an equally insuperable obstacle to the evidentiary hearing that Weidner asks us to have the district court convene. As to the risk the affidavit process poses to the finality and integrity of judgments, this concern applies with diminished force in habeas proceedings, which are premised on the proposition that “[cjonventional notions of finality of litigation have no place where life or liberty is at stake and infringement of constitutional rights is alleged.”
Sanders v. United States,
373 U.S. 1, 8, 83 S.Ct. 1068, 1073, 10 L.Ed.2d 148 (1963). Turning to the last of the doubts about judicial testimony expressed in
Strickland,
comity between state and federal courts, we think that the affidavit procedure we recommended to the district court in
Weidner I
responds to these concerns in a way that the live testimony at issue in
Strickland
did not. As we observed in
Weidner I,
“it would be unseemly for a federal district judge to summon the state trial judge as a witness in a federal habeas corpus proceeding to give testimony and be cross-exam-ined_” 866 F.2d at 963. Under the affidavit procedure we recommended, however, the state trial judge furnished his evidence in affidavit form, and did so voluntarily. Had he chosen not to comply, the district court would have had no choice but to hear the testimony of the participants in Weidner’s interrogation himself and make his own findings of fact.
We nevertheless share the concerns raised by judicial testimony concerning mental processes expressed in
Fayerweather
and
Strickland
and supported by the insights into human memory and cognition presented by the Habers. These concerns dictate that recourse to the testimony of a state trial judge concerning the mental processes that underlay his ruling should be had only in the unfortunate circumstance when the reasons supporting the ruling are wholly unavailable from the record. Even then, the certifications or affidavits must be carefully evaluated to determine if they are consistent with relevant record evidence. Where state trial judges fail to adequately develop the relevant facts so that not even implicit findings,
see Marshall v. Lonberger,
459 U.S. 422, 433, 103 S.Ct. 843, 850, 74 L.Ed.2d 646 (1983), can be gleaned from the record, the habeas procedure is better served by a de novo hearing than by allowing state judges to cast their minds back to the state trial. At the very least, nothing in this opinion or our prior opinion in
Weidner I
should be read as limiting the use of de novo hearings in favor of affidavits or certifications submitted by state trial judges.
That being said, we are compelled to conclude that we did not clearly err in
Weidner I
when we instructed the district court that its hearing of Weidner’s habeas petition could consist of an affidavit of the state trial judge who ruled that his confession was voluntary, whether or not as an initial matter we would have opted for the same procedure. The trial judge’s second affidavit in this case set out with particularity his findings of fact, none of which are contradicted by the testimony of witnesses at the motion to suppress. We note in passing that it is also at least questionable whether the affidavit procedure worked a substantial injustice on Weidner. As we noted in
Weidner I,
there is no “serious question that Weidner was guilty of the grave crimes of which he was convicted.” 866 F.2d at 963. Weidner’s two codefend-ants also confessed, and their confessions corroborated Weidner's, raising the possibility that even if Weidner's confession was coerced, its admission at trial would have been harmless error.
See Arizona v. Fulminante,
— U.S. -, 111 S.Ct. 1246, 1265, 113 L.Ed.2d 302 (1991).
III. CONCLUSION
Because neither the new evidence presented on remand in this case nor the
asserted errors in our prior opinion convince us that the affidavit procedure we recommended in that opinion should not remain the law of the case, and because the district court complied with our mandate on remand, its decision to deny Weidner’s petition for habeas corpus is
Affirmed.