This is an appeal by Jose Lopez, a state prisoner, _from the denial by the federal district court of his habeas corpus petition. The central issue concerns the delayed disclosure to Lopez of information helpful to his defense. We recount briefly the *592factual background and prior proceedings, reserving certain details for later discussion.
Lopez met Maria Rodriguez in July 1993 and, soon thereafter, began to live with Rodriguez and her two sons in Haverhill, Massachusetts. Lopez and Rodriguez quarreled and she obtained a protection order against him but she also allowed him on occasion to stay at her apartment. On June 28, 1994, they quarreled again after Rodriguez was paid to enter into a sham marriage with a man who sought U.S. citizenship.
Lopez left the apartment after this quarrel but returned early in the morning on June 29. In the afternoon of the 29th, Rodriguez left the apartment, leaving Lopez to watch after her son Danny, age seven, who was then playing at a neighbor’s house. Later in the afternoon, Lopez picked up Danny in his truck. Lopez returned to the apartment in the evening without Danny and said he did not know where Danny had gone.
On June 30, police searched an apartment that Lopez had visited on the afternoon Danny had disappeared and recovered certain items, including pants that Lopez had been wearing on the prior day which were now wet. From his truck, they recovered a piece of rope. On the same day, Lopez was arrested.
Danny’s body was discovered at a salvage yard in Haverhill on July 8, 1994, in the trunk of a white car that was marked to be destroyed. A 100-pound transmission had been used to weight down Danny’s body, and rope was wrapped around his neck and tied to the hinges of the trunk. Lopez, the police learned, had visited the yard about 10 days before, looking for a transmission, and had been directed to the area where the body was thereafter found.
Lopez was tried for Danny’s murder and for kidnapping. In addition to the evidence described above, the Commonwealth showed by medical testimony that Danny had died around the time of his disappearance and that paint smears from a screwdriver found in Lopez’ truck were consistent with paint on the car in which Danny was found, that two sets of fibers linked Danny to Lopez’ truck, and that Lopez’ pants contained white paint chips, iron and rust stains and also red fibers that matched those on Danny’s shirt.
Julia Diaz, a friend of Rodriguez’ who was acquainted with Lopez, testified that Lopez had told her that, if Rodriguez left him, he would “hurt [Rodriguez] where it hurts the most.” According to Diaz, Lopez told her a story about a couple “having problems,” which led the man to hide the woman’s children for a few days, returning the children only once the couple “got back together.”
The Commonwealth also presented testimony from Angel Miranda, Lopez’ cellmate during his wait for trial. Miranda testified that Lopez had confessed to Miranda that he (Lopez) had offered Danny “ten dollars, driven him to a junkyard, strangled him with a brown towel until he was unconscious, and placed him inside the trunk of a car ‘marked to be crushed,’ with a transmission on top of him.” Commonwealth v. Lopez, 433 Mass. 406, 742 N.E.2d 1067,1070 (2001).
Lopez did not testify but, through other witnesses, sought to establish that he had been close to and cared about the boys; that without Danny he (Lopez) had been seen at a number of places and spent time with various individuals on the afternoon of the disappearance; that he worked with cars and patronized the junkyard in question on other occasions; and (through an expert) that the state’s forensic evidence— paint, rust and fiber — was not conclusive.
*593One other line of evidence offered in Lopez’ defense is directly pertinent to this appeal. Lopez’ trial had begun on July 12, 1996, and the prosecution’s case in chief had ended on July 17. On July 18, when the defense began to present its case, the prosecutor, Kevin Mitchell, learned from Massachusetts State Police Sergeant John Garvin that a Haverhill police officer had received a phone call on July 17 from one John Roche, who had information regarding Lopez’ case. Mitchell directed Garvin to create a report summarizing the call and upon receipt gave the report to Lopez’ counsel.
Roche testified on July 28, 1996, as a defense witness, that he lived on a road abutting the salvage yard and that he had observed a suspicious truck on the road in the last week of June 1994. There were three people in the truck, one of whom was “stocky, bald and Spanish.” Roche also said that he had told the Haverhill police of this fact on July 3, 1994, and had recontacted the police during the trial to repeat this information because they had apparently not followed up on it.1
Ronald Parolisi, captain of the Haverhill police, then testified that the person described by Roche “sounded like a local person that [the police] know as Kojak,” who was suspected of dealing drugs, and that Kojak had not been a subject of the murder investigation. In his closing, Lopez seized on Roche’s and Parolisi’s testimony, suggesting that Kojak — perhaps along with Rodriguez — had killed Danny and disposed of the body.
The jury convicted Lopez of both murder and kidnapping, the former resulting in a mandatory life sentence. See Mass. Gen. Laws ch. 265, § 2 (1994). Lopez then sought a new trial based on allegedly new evidence, specifically, that “Kojak” was a drug dealer named Juan Garcia, that Roche had now identified a photograph of Garcia as one of the men he had seen in the truck near the junkyard, and that — to Lopez’ own knowledge — Garcia had supplied drugs to Rodriguez and had vowed to have revenge against Lopez after a fight between Garcia and Lopez.
The trial judge denied the new-trial motion, saying that he did not see “a substantial risk that, [if] the jury [were] exposed to [the Garcia-Kojak] evidence, [it] would have reached a different conclusion.”2 See Lopez, 742 N.E.2d at 1074. The Supreme Judicial Court affirmed, saying that there was “no evidence” that Garcia was involved in Danny’s murder, that Roche had been vague about when he saw Garcia, and that the only link of Garcia to the crime was Lopez’ own self-serving affidavit. Id. The decision concluded:
Merely introducing another possible suspect, without substantial admissible evidence that this person, and not the defendant, may have committed the crimes, does not warrant a new trial. Here, the possibility of Garcia as an alternate suspect was presented to some extent at trial, and rejected by the jury. The little additional and generalized information contained in the defendant’s postconviction affidavits casts no real *594doubt on the validity of the jury’s verdicts.
Id. at 1074-75 (footnote omitted).
Lopez then filed a petition for habeas corpus in the federal district court including a claim that the Kojak evidence had been wrongfully withheld by the police in violation of the Brady doctrine, see Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), and the district court ordered an evidentiary hearing. Lopez v. Massachusetts, 349 F.Supp.2d 109, 126 (D.Mass.2004). At the four-day hearing, there was testimony from Roche, Lopez, Garcia, trial prosecutor Kevin Mitchell, and Haverhill police officer Todd Smith.3
At the close of the hearing, on March 1, 2006, the district court judge ruled from the bench. He denied the petition, saying inter alia
•that he largely credited Roche’s testimony, although he thought that Roche’s identification of Garcia as the man in the truck may have resulted from a suggestive identification process by the defense;
•that he was not persuaded by Lopez [apparently referring to Lopez’ attempt to link Garcia to Rodriguez and Lopez’ claim of a prior quarrel between him and Garcia];
•that he could not conclude “that any of the facts upon which [the state courts had] based their legal rulings were unreasonable as a matter of law”; and
•that Lopez had had it within his knowledge to provide the information needed to pursue “any additional followups” [apparently meaning that when Kojak’s name first surfaced, Lopez could have made the connection and offered the exculpatory information about drug dealing and the alleged quarrel].
The district court granted a certificate of appealability, 28 U.S.C. § 2253(c) (2000); Fed. R.App. P. 22(b)(1), and Lopez appealed to this court. The question before us, broadly framed, is whether there was a Brady violation warranting Lopez’ release, subject always to the right of the state to retry him. Where the state court has resolved a constitutional issue, the habeas court must defer within specified limits to judgments by the state court as to issues of both law and fact. See 28 U.S.C. § 2254(d)(1), (e)(1).
The Brady issue was raised in the state proceedings, but the state courts relied not on federal precedent but on state-law cases; nor did they phrase their grounds for rejecting a new trial in traditional Brady terms. See Lopez, 742 N.E.2d at 1073-75. Neither of these facts necessarily precludes deference, see Gipson v. Jordan, 376 F.3d 1193, 1196-97 & n. 1, 1200-05 (10th Cir.2004), cert. denied, — U.S. -, 126 S.Ct. 729, 163 L.Ed.2d 567 (2005); see also Early v. Packer, 537 U.S. 3, 8, 123 S.Ct. 362, 154 L.Ed.2d 263 (2002), but we bypass the issue because the result is the same even if no deference is accorded.
Under Brady, the prosecutor has a duty to make available to the defense exculpatory evidence, including evidence useful for impeachment, possessed by the prosecution team or its agents. Giglio v. United States, 405 U.S. 150, 153-54, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972); Brady, 373 U.S. at 87, 83 S.Ct. 1194. Roche’s evidence was certainly helpful to the defense — how helpful is a separate issue — but it was turned over and Lopez made use of it both through Roche and in closing. So the *595evidence possessed by the prosecutor was turned over — but only in mid-trial.
On this appeal, the Commonwealth argues that although circuit precedent has applied Brady to cases of delayed disclosure, see United States v. Lemmerer, 277 F.3d 579, 584 (1st Cir.), cert. denied, 537 U.S. 901, 123 S.Ct. 217, 154 L.Ed.2d 173 (2002), no Supreme Court case does so. Accordingly the Commonwealth argues, the state court in denying relief cannot be accused of an unreasonable application of clearly established Supreme Court precedent. See Carey v. Musladin, — U.S. -, 127 S.Ct. 649, 166 L.Ed.2d 482 (2006). The Commonwealth’s blanket position limiting Brady to complete non-disclosure is mistaken.
It could not, for example, comport with Brady’s duty to disclose to say that a prosecutor could choose to sit on vital exculpatory evidence for six months and belatedly turn it over to the defense in mid-trial too late to be effectively used. Depending upon all kinds of circumstances, delayed release may not be a violation or it may mitigate a prior withholding; but to treat Brady as mechanically limited solely to complete non-disclosure would be foolish and not “reasonable.”
However, the non-disclosure claim in this case is less straightforward, whether couched as delay or complete non-disclosure. The prosecutor turned over the information from the second call to the state police about as fast as could be expected. So to make out a Brady violation depends at the outset on showing that the first call should have been disclosed in a more timely fashion' — specifically, that the prosecutor is responsible for what Smith knew and that Smith should have regarded as exculpatory the somewhat vague and unpromising initial call from Roche.
Both issues raise interesting questions not addressed by Lopez in his brief and only indirectly adverted to by the Commonwealth and the state courts.4 We need not pursue them because even a wrongful withholding of evidence is not a basis for Brady relief unless it was prejudicial, meaning (in this context) either a likelihood of a different result or circumstances that otherwise shake a court’s confidence in the result of the trial. See Strickler v. Greene, 527 U.S. 263, 281, 119 S.Ct. 1936, 144 L.Ed.2d 286 (1999); Kyles v. Whitley, 514 U.S. 419, 434, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995).
The evidence against Lopez was largely circumstantial but very strong. Indeed, it was more than circumstantial if one gives significant weight to Lopez’ supposed confession to Miranda. But absent corroboration (e.g., by a tape recording of the confession or a newly revealed detail), alleged confessions to cellmates are often to be treated very skeptically, given the incentives to lie and the limited ability to cross-examine a witness who claims no firsthand knowledge of anything but the supposed confession.5 Miranda later recanted his testimony.
But the circumstantial evidence of Lopez’ guilt — motive, opportunity and foren*596sic ties — was even stronger than our outline of the main facts indicates. Just prior to Danny’s disappearance, Lopez had had a serious quarrel with Rodriguez and a clear motive to retaliate. Further, according to Diaz, Rodriguez had virtually outlined such a course of revenge on a child — to the extent at least of kidnapping — after a quarrel with Rodriguez in 1993.
As for opportunity, Lopez had admittedly made contact with Danny during the afternoon in question; he said afterwards that he called Danny away from the neighbor to help him close a window — itself a somewhat surprising explanation — but he denied that Danny had left with him in his truck. However, a neighbor had seen Danny getting into the truck with Lopez on that afternoon.
The evidence showed that Lopez was familiar not only with the junkyard but with the very location where Danny’s body was found in a car. And the forensic evidence linking Lopez with the crime was considerable. The state court’s summary on this point is telling:
Paint smears taken from a screwdriver found in the defendant’s truck matched the paint on the automobile in which the body was found. Fibers consistent with those from the victim’s multicolored shorts were found in the defendant’s truck, and black fibers consistent with the truck’s carpet were found on the victim’s sandals. In addition, the defendant’s black pants contained stains of iron and rust, white paint chips, and red fibers consistent with those from the victim’s hooded shirt.
Lopez, 742 N.E.2d at 1070.
The defense offered some counters — Lopez’ supposed affection for the children, incomplete alibi evidence, and an attack on the state’s forensics — but the Commonwealth’s case was assuredly a strong one, even disregarding Miranda. Further, Roche’s main story, including the identification of “Kojak” by a police witness at the trial, was made available to the jury. Let us see just what is added by what Lopez claims to be new evidence.
The single critical fact that could have helped Lopez appreciably is testimony that Garcia — in addition to knowing Rodriguez — had a strong motive to kill her child; and Lopez’ basis for this was a supposed quarrel between Lopez and Garcia. Even so, it would take a pretty remarkable leap for the jury to think that Garcia would revenge himself by killing an innocent child to frame Lopez when he could more simply have killed Lopez himself.
And, there is a further difficulty. Garcia, as we now know, would have testified at trial that he did not even know Lopez. Lopez could not have countered him at trial with an affidavit; Lopez himself would have had to testify to the contrary. This in turn would have opened Lopez to cross-examination on a host of issues that could easily have been devastating, ranging from the lie about Danny not getting into his truck to gaps in his alibi evidence to the multi-strand forensic evidence and wet pants. •
It is far from certain that Lopez would have taken this risk — even with the added incentive of Roche’s later clear-cut (if suspect) identification of Garcia as the man Roche had seen. And, if Lopez had testified, it is uncertain that the jury would *597have believed him (the district judge did not) and even more uncertain that it would have thought Garcia’s quarrel (if it occurred) was a plausible motive for Garcia to kill Danny.
Of course, to acquit Lopez, it would have been enough for him to raise a reasonable doubt; but, as against the quite strong circumstantial case against Lopez, the very most that Lopez’ testimony could have shown about Garcia as an alternative suspect is far from strong; and by testifying Lopez could easily have made his position much worse. We understand why the district court held a hearing but our confidence in the verdict is not at all shaken.
Affirmed.