OPINION EN BANC
BOUDIN, Chief Judge.The facts underlying this section 2255 action, recounted in detail in prior opinions,1 can be briefly summarized. About eight years ago, on January 25, 1995, a shooting occurred in the early morning hours in Boston, and there ensued a police chase of several suspects in a Lexus. Eventually, the Lexus was trapped in a dead-end street. Pulling up on the left side of the Lexus — the first of many pursuing police vehicles — was an unmarked police car with two plainclothes officers. One of the officers, Michael Cox, ran from the car after a suspect named Robert Brown who was fleeing on foot from the Lexus toward a fence to the right of the Lexus.
By this time other police cars were arriving, pulling in next to and behind the Lexus. In this line was a car driven by Officer Richard Walker; behind him was one containing Officer Kenneth Conley and his partner. According to later testimony, Cox chased Brown to the fence and grabbed at Brown but Brown got over. As Cox stood at the fence, he was brutally attacked and beaten by other arriving police officers who thought he was one of the *10suspects (and who also thought, wrongly, that a policeman had been shot). The assaulting officers discovered their mistake and dispersed, leaving Cox badly injured.
In April 1997, a federal grand jury began an investigation into the assault. Cox had not seen the officers who beat him and, although many officers had been at the scene, information was not readily provided. In due course, Conley was called before the grand jury. Conley testified that he had seen no one beating Cox; that he had himself pursued Brown to the fence; that he had seen no one between him and Brown and no one grabbing at Brown; that he had pursued Brown on the other side of the fence; and that after a chase of about a mile, he had caught and arrested Brown. There is little doubt that Conley did chase and catch Brown, but prosecutors did not believe the rest of his story.
In August 1997, the grand jury indicted Conley for perjury and obstructing justice—in substance, for denying that he saw Cox pursue Brown to the fence and for denying that he saw Cox being beaten. 18 U.S.C. §§ 1503, 1623 (2000). At Conley’s trial in June 1998, three witnesses for the government (Cox, Brown and Walker) testified that Cox chased Brown to the fence and grabbed at Brown unsuccessfully as Brown scaled it. Brown also said that after he landed, he saw Conley through the fence and saw other officers (but not Conley) beating Cox. He also identified Conley as the officer who had chased and arrested him. Conley did not testify.
The jury convicted Conley of lying, and of obstructing justice, in testifying that he had seen no one else pursuing Brown to the fence; as for the charge that Conley had lied in denying seeing Cox being beaten, the jury acquitted Conley. Conley was sentenced to just under three years in prison. The sentence was stayed, and to date Conley has not served any of this sentence. No policeman was indicted or convicted of the beating, although three officers—but not Conley—were found liable to Cox in a civil trial following Conley’s criminal trial.
On direct appeal, this court in 1999 affirmed the conviction. Conley I, 186 F.3d at 26. After the affirmance, Conley in early 2000 moved for a new trial under Fed.R.Crim.P. 33. Conley identified a number of pieces of evidence that he claimed were either newly discovered or wrongly withheld by the prosecution. Most of the evidence would have been useful (if useful at all) to impeach Officer Walker and—in one instance—Brown. One other piece of evidence, comprising the civil trial testimony of a security guard named Charles Bullard who was riding with Cox, might (in Conley’s view) have suggested that Cox could have ended up behind Conley during the chase to the fence.
Under Rule 33, a new trial in “the interests of justice” may be granted liberally on a motion made “within 7 days” after the verdict; but, thereafter, it can be granted solely for newly-discovered evidence (and then only on a motion made within three years). Fed.R.Crim.P. 33. Further, under the case law, the defendant who makes such a motion after seven days bears the heavy burden of showing that the evidence would probably result in an acquittal upon retrial. United States v. Wright, 625 F.2d 1017, 1019 (1st Cir.1980). But if the new evidence was wrongly withheld by the government in violation of its obligations under Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), it is enough to show that the evidence undermines confidence in the verdict. Kyles v. Whitley, 514 U.S. 419, 435, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995).
*11In its decision on the Rule 33 motion in June 2000, the district court discussed the alleged new evidence at some length and concluded that material new evidence had first become available to defense counsel only after trial, Conley II, 103 F.Supp.2d at 51-58; the court was less clear as to whether any had been wrongly withheld in violation of Brady. Id. at 51-52, 54-55. In any event, it ordered a new trial in “the interests of justice,” without finding prejudice under either Wright or Brady. Id. at 58. Somewhat cryptically, the district court stated in conclusion:
I conclude that the answer to the second question stated above [the extent of prejudice] cannot be determined as a matter of law, under ... [Wright and Brady ]. Instead, in the unique circumstances of this case, I conclude that the determination to allow or not to allow a new trial is one committed to an exercise of discretion by the court to which the legal system assigns responsibility for making the determination.
Id. (emphasis added).
On appeal by the government, this court held in May 2001 that because the motion for a new trial was made more than seven days after the verdict, the district court could not use the general “interests of justice” standard in Rule 33 to bypass the established Wright and Brady prejudice requirements. Conley III, 249 F.3d at 46. We understandably said that there was no need for us to analyze the evidence ourselves under Wright and Brady or to remand for the district court to do so; our reason was that we read the district court’s “as a matter of law” statement quoted above as its own ruling that the Wright and Brady tests had not been met. Id.
Conley then filed the present motion in the district court under 28 U.S.C. § 2255 (2000), based (more or less) on the same newly-discovered evidence. In September 2001, the district court granted the section 2255 motion, setting aside the conviction and ordering a new trial. Conley IV, 164 F.Supp.2d at 223-24. In doing so, the district court said that it was applying the Wright test, which it deemed to have been mandated by this court’s earlier decision on the Rule 33 motion. Id. at 222. The district court found expressly that the new evidence was so powerful that it would probably cause an acquittal on retrial. Id. at 223. The district court never reached Conley’s Brady claim because it found that a new trial was required under Wright. Id. at 222.
On the government’s appeal, a divided panel of this court again reversed the district court. The panel majority said that the district court had decided in its earlier Rule 33 decision (Conley II) that the Wright and Brady standards could not be satisfied and that, on review (in Conley III), this court had declined to remand, ruling that the sentence should now be executed. The panel majority therefore held that the district court’s ruling on the section 2255 motion was inconsistent with the law of the case doctrine. Again, the panel declined to address on the merits Conley’s new evidence claims under Wright and Brady.
The en banc court then granted Conley’s petition for rehearing, withdrawing (as is customary) the panel decision. We now hold that the law of the case doctrine has no application here and also that Brady but not Wright applies to new evidence claims made in a section 2255 motion. This leads us to vacate the district court’s section 2255 decision and to remand so that Conley can obtain a ruling on his Brady claim. We decline to decide the Brady claim ourselves in the first instance.
*12We start with the law of the case doctrine on which the government continues to rely. The law of the case doctrine has two branches: one provides that, subject to exceptions, e.g., United States v. Bell, 988 F.2d 247, 251 (1st Cir.1993), a court must respect and follow its own rulings made at a prior stage in the same case; the other branch' — -sometimes known as the mandate rule — far more stringently precludes a lower court from contravening the rulings of a higher court made at an earlier stage of the same controversy.2 The difference is cogently described in our recent decision in Ellis v. United States, 313 F.3d 636, 646-48 (1st Cir.2002).
At the time that we decided Conley III, our reading of the district court’s Rule 33 decision there under review (Conley II) was surely a plausible one. The district court had made clear in its own decision that it was not making a prejudice finding under Wright or Brady (“cannot be determined as a matter of law”) and it invoked “the unique circumstances of this case” to justify an “exercise of discretion” to grant a new trial — without reliance upon Wright or Brady. Conley II, 103 F.Supp.2d at 58. If there were prejudice under Wright and Brady — one might ask- — why would the district court have invented its own standard? And, if the district court had decided the Wright and Brady issues in Conley II, law of the case doctrine would constrain its ability to revisit the issues now.
Yet the district court does not think its own opinion in Conley II was intended to resolve the Wright and Brady issues. Invoking Wright, the district court now reaches a result opposite to the one we attributed to its Conley II decision; and nothing suggests that the district court regards this as a contradiction of Conley II.3 Of course, the district court knows better than we do what it originally meant in Conley II. See Garrity v. Sununu, 752 F.2d 727, 731 n. 4 (1st Cir.1984). In hindsight, it is now clear that Conley II’s language — on which we relied in Conley III — is ambiguous as to whether it represented a finding of no prejudice under Wright and Brady.
What the district court said in Conley II was that the answer to the prejudice question under Wright and Brady “cannot be determined as a matter of law....” Conley II, 103 F.Supp.2d at 58. Although in Conley III we understandably read this to mean that there was no such prejudice, the phrase “as a matter of law” can be used to say that an issue is not susceptible to being resolved on the existing record and that an evidentiary hearing or additional information is needed for its resolution. See, e.g., Fed.R.Civ.P. 56(c). This is probably the most plausible reading, for it reconciles the district court’s decision in Conley II with its latest decision.
This leads us to conclude that the district court’s latest decision does not impermissibly contradict its own earlier ruling in Conley II: having been told by this court in Conley III that it could not create its own standard for “unique” circumstances, it has now simply decided an issue (Wright) that it bypassed in its earlier decision. But the fact remains that we ourselves in Conley III read Conley II as *13deciding that prejudice under Wright and Brady could not be established. Is our assumption — even if now seen to be mistaken — itself binding on the district court under the mandate-rule branch of law of the case?
One might argue that a prior assumption by an appellate court as to what the district court meant should not be treated as law of the case, which is normally understood as directed to substantive legal rulings. But an interpretation of a lower court decision can be as much a contested issue as the interpretation of a contract. We are reluctant to agree that such an interpretation — at least if it was fully litigated and not merely assumed en passant, see Platoro, Ltd. v. Unidentified Remains of Vessel, 695 F.2d 893, 898 n. 4 (5th Cir.), cert. denied, 464 U.S. 818, 104 S.Ct. 77, 78 L.Ed.2d 89 (1983)—is exempt from normal law of the case doctrine.4 There is a better reason for refusing to perpetuate what now seems to have been a mistake.
Law of the case is not a straitjacket but can be avoided — at the direction of the court that made the invoked ruling — on several different bases. Ellis, 313 F.3d at 647-48. Two of the grounds permitting a deviation from law of the case are where there has been a change in prevailing law or where there is new evidence on the question at issue. Id. For example, in United States v. Robinson, 690 F.2d 869, 872-73 (11th Cir.1982), the Eleventh Circuit revisited its own prior reli-anee on a magistrate judge’s finding after the latter clarified and expanded upon his ruling.5
Whether one characterizes the district court’s new decision as new law or new evidence, it is certainly a new circumstance justifying a fresh look by us at the question whether the district court previously resolved the Wright and Brady claims on the merits. Having reexamined the matter, we think the district court has not so resolved them, despite our earlier assumption that it had. It is equally clear that this court has never decided those claims on the merits; instead, we adverted briefly to some of the issues raised. Conley III, 249 F.3d at 43, 46-47.
This brings us to the substance of the district court’s section 2255 decision. In a nutshell, the district court ruled on this go-around that “a new trial is to be allowed under the Wright test, and because this determination controls the judgment to be ordered, I do not consider further the Brady test.” Conley IV, 164 F.Supp.2d at 222. It then found that the newly discovered evidence “would have greatly enhanced” the defense case; that it “strikes at the heart of the prosecution’s case”; and that Conley had shown “a probable result of acquittal in a new trial.” Id. at 223.
The problem is that new evidence claims under Wright are cognizable grounds of relief only in post-trial motions for a new trial and not under habeas or its *14section 2255 surrogate. Powerful new evidence of innocence can satisfy one of the new “gatekeeper” requirements for bringing a “second or successive” section 2255 motion, see 28 U.S.C. § 2255; but a traditional habeas ground is required once one gets through the gate. Merely to claim that new evidence casts doubt, even grave doubt, on the correctness of a conviction is not a ground for relief on collateral attack. See Herrera v. Collins, 506 U.S. 390, 400, 113 S.Ct. 853, 122 L.Ed.2d 203 (1993); United States v. Evans, 224 F.3d 670, 673-74 (7th Cir.2000).6
Conceivably, the Wright claim could be reawakened if we withdrew sua sponte our mandate in Conley III, an issue we asked the parties to brief. Although this course might first appear to be at odds with Calderon v. Thompson, 523 U.S. 538, 554-58, 118 S.Ct. 1489, 140 L.Ed.2d 728 (1998), we think that Calderon is distinguishable. Calderon’s holding was explicitly directed at the recall of a “mandate [in a habeas proceeding in order] to revisit the merits of an earlier decision denying habeas corpus relief to a state prisoner.... ” Id. at 558, 118 S.Ct. 1489. The considerations are somewhat different where, as here, we are concerned with intra-federal proceedings and, more importantly, where the Conley III mandate was not issued in a habeas proceeding at all but on direct review of the denial of a new trial motion.
Nevertheless, independent of Calderon, recall of a mandate — other than to correct a clerical error — threatens important interests in finality and is a step to be taken only in the most unusual circumstances.7 Defense counsel in Conley III chose in the first instance not to argue for a remand, possibly in part because of a deliberate tactical choice (see note 4 above). Further, so far as we can tell at this stage, the “new evidence” while arguably helpful to Conley serves more to raise doubts than to establish innocence or a “clear probability” of an acquittal; serious doubts may be enough if Brady evidence was withheld but (as already explained) is not normally sufficient under Wright. Given these circumstances, we do not see how a sua sponte withdrawal of the mandate can be justified.
This leaves open only Conley’s claim under Brady, a settled basis for collateral attack. See Barrett v. United States, 965 F.2d 1184, 1189 (1st Cir.1992). Indeed, claims based on new evidence wrongfully withheld can prevail on a lesser showing of prejudice than claims based on newly-discovered evidence (because the former assumes government misconduct). See United States v. Gonzalez-Gonzalez, 258 F.3d 16, 20 (1st Cir.2001). But, of course, not all newly-discovered evidence fits within Brady: the evidence must, at a bare minimum, have been within the government’s grasp and wrongly withheld from the defense. Brady, 373 U.S. at 87, 83 S.Ct. 1194. Perhaps some, but seemingly not all, of Conley’s new evidence falls within this class.
The government asserts that whether viewed through the lens of Wright or Brady, the new evidence is so thin that we *15should ourselves decide without further ado that a new trial is unjustified. Conley’s counsel says that we should affirm the trial judge’s directly contrary assessment, or, in the alternative, remand the matter to the same district judge, who has already said that the new evidence claim under Wright is persuasive and might well say the same under Brady. Although reluctant to prolong this long-lived litigation, we have concluded that neither course is appropriate.
The evidence underlying the Brady claim has never been systematically assembled and fully analyzed in any court in any of the various decisions to date. There are fragments of discussion in several of the district court decisions, Conley IV, 164 F.Supp.2d at 221-23; Conley II, 103 F.Supp.2d at 51-58; but nowhere are all of the items of supposed new evidence set forth, their significance considered, their status assessed under Brady, and a judgment made (based on a review of all of the evidence in the entire trial) as to whether the Brady-qualifying items of new evidence (taken together) undermine confidence in the verdict.
Save in the most straightforward case, an en banc court is not the best initial forum for this kind of undertaking. Some Brady issues can require fact-finding as to what the government knew and when it knew it. And, where (as here) the case was circumstantial and much of the evidence concerns arguable impeachment of key witnesses, en banc review is generally assisted by having a well-worked-out district court assessment before the appellate court attempts its own evaluation.
At the same time, we agree with the government that it is time for another district judge to consider the new evidence claim afresh. Although this court has clear authority to order that further proceedings be conducted before a different judge, see 28 U.S.C. § 2106 (2000); Liteky v. United States, 510 U.S. 540, 554, 114 S.Ct. 1147, 127 L.Ed.2d 474 (1994), we normally defer to the district court’s own reassignment policies.8 However, in this instance the circumstances are unusual: the district judge has now twice said that he believes a new trial to be warranted and we have twice reversed or vacated his decision for errors of law antecedent to an assessment of the evidence.
A third remand would put the district judge in a very awkward position. If he ordered a new trial yet again, it might be thought that he was wedded to an outcome; if he altered his result, Conley might suppose that the judge had yielded to exhaustion or to a supposed message from this court. We have no doubt about the good faith of the district judge, but in the peculiar circumstances of this case a fresh look is warranted, despite the cost of requiring a new district judge to master this record.
A concluding word should be said about the duration of this case, a point emphasized in the prosecution’s brief. A pattern of long delays in deciding criminal cases, or civil ones for that matter, should certainly be a matter of concern for any court. But in an individual appeal, especially in a criminal case with liberty and honor at stake, the main concern is always the achievement of justice. Justice includes the interests of the state as well as the defendant, but just where justice lies in this case is less clear than the government may suppose.
*16The government’s evidence at trial was assuredly adequate for conviction, but it was always circumstantial because no one testified that he or she saw Conley looking at Cox in pursuit of Brown and Conley never admitted seeing him. The inferences for this circumstantial case depended importantly on testimony as to the position of different actors at different times in a confused and changing scene in the dark of night. Whether impeachment or other evidence was wrongfully withheld and, if so, whether its existence shakes confidence in the jury’s verdict are questions for remand, but they are questions worth answering with care, whatever time it takes to answer them.
The district court’s order granting the section 2255 motion is vacated and the matter is remanded to the district court for reassignment to a new judge in accordance with local procedures and thereafter for further proceedings consistent with this opinion.
It is so ordered.
. United States v. Conley, 186 F.3d 7 (1st Cir.1999) (‘‘Conley I"), cert. denied, 529 U.S. 1017, 120 S.Ct. 1417, 146 L.Ed.2d 310 (2000); United States v. Conley, 103 F.Supp.2d 45 (D.Mass.2000) ("Conley II”); United States v. Conley, 249 F.3d 38 (1st Cir.2001) (‘‘Conley III"); Conley v. United States, 164 F.Supp.2d 216 (D.Mass.2001) (‘‘Conley IV”).
. Arizona v. California, 460 U.S. 605, 618, 103 S.Ct. 1382, 75 L.Ed.2d 318 (1983); NLRB v. Goodless Bros. Elec. Co., 285 F.3d 102, 107 (1st Cir.2002); Knapp Shoes, Inc. v. Sylvania Shoe Mfg. Corp., 72 F.3d 190, 197-98 (1st Cir.1995), cert. denied, 517 U.S. 1245, 116 S.Ct. 2500, 135 L.Ed.2d 191 (1996).
. The district court's newest opinion does make a passing reference to additional new evidence, Conley IV, 164 F.Supp.2d at 221, but it does not describe any new evidence, let alone hold that it is new evidence that tips the balance.
. Whether the issue was fully litigated in Conley III could be disputed. The government said that the district court had ruled in Conley II that no prejudice existed; Conley’s counsel urged — much less plausibly — that the district court's "discretionary” grant of a new trial rested in substance on Wright or Brady. The possibility that the district court was simply bypassing Wright and Brady seems not to have been argued by anyone, perhaps because it would have justified a remand where both sides wished to prevail outright — Conley by affirmance and the government by outright reversal.
. Other circuits are in accord on the general principle. See Benson v. SI Handling Sys., Inc., 188 F.3d 780, 783 (7th Cir.1999); Browning v. Navarro, 887 F.2d 553, 556 (5th Cir.1989); United States v. Cirami, 563 F.2d 26 (2d Cir.1977).
. It is not clear whether a habeas claim could be based on. new evidence proving actual innocence, see Herrera, 506 U.S. at 417, 113 S.Ct. 853; but Conley is not close to such a showing. At best, the newly-discovered evidence, adding everything together, simply increases — how much is debatable — the likelihood that at a new trial a jury might find reasonable doubt of guilt and so acquit.
. See Boston & Me. Corp. v. Town of Hampton, 7 F.3d 281, 283 (1st Cir.1993); Fine v. Bellefonte Underwriters Ins. Co., 758 F.2d 50, 52-54 (2d Cir.), cert. denied 469 U.S. 874, 105 S.Ct. 233, 83 L.Ed.2d 162 (1984); 16 Wright, Miller & Cooper, Federal Practice and Procedure § 3938, at 712 (2d ed.1996) (describing "profound interests in repose”).
. In four of the five districts in this circuit, including Massachusetts, there are formal district court rules governing reassignment, e.g., D. Mass. R. 40.1(K). In all districts, judges sometimes ask for reassignment of a remanded case even when not compelled to do so.