dissenting in part.
We do not need to know whether or not Donald McLaurin had a deal that charges would not be pressed against him or his probation revoked for anything he did on the weekend of October 10th,1 because even if there were a deal, evidence of it would not have changed the outcome of Horton’s trial. The California Supreme Court denied this claim on the merits, but as it did so without discussion, we independently review the record to determine whether its decision was objectively reasonable. See Delgado v. Lewis, 223 F.3d 976, 982 (9th Cir.2000); Pirtle v. Morgan, 313 F.3d 1160, 1167 (9th Cir.2002) (noting that although we independently review the record, we still defer to the state court’s ultimate decision). The district court assumed (as do I) that an undisclosed deal had been made, but rejected Horton’s Brady claim because the suppressed evidence was not material. Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963). I agree, and would hold that the state court’s decision was not contrary to, or an unreasonable application of, clearly established United States Supreme Court law.
*583Evidence is material “if there is a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different.” Strickler v. Greene, 527 U.S. 263, 280, 119 S.Ct. 1936, 144 L.Ed.2d 286 (1999) (citing United States v. Bagley, 473 U.S. 667, 676, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985), and Kyles v. Whitley, 514 U.S. 419, 433-34, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995)). “[T]he question is not whether the defendant would more likely than not have received a different verdict with the evidence, but whether in its absence he received a fair trial, understood as a trial resulting in a verdict worthy of confidence.” Strickler, 527 U.S. at 289-90, 119 S.Ct. 1936 (citing Kyles, 514 U.S. at 434, 115 S.Ct. 1555). Put differently, “the question is whether ‘the favorable evidence could reasonably be taken to put the whole case in such a different light as to undermine confidence in the verdict.’ ” Id. (quoting Kyles, 514 U.S. at 435, 115 S.Ct. 1555).
Evidence of the deal that McLaurin declares he had would not put the entire case in such a different light that my confidence in the outcome is undermined. Benn v. Lambert, 283 F.3d 1040, 1053 (9th Cir.2002) (citing Bagley, 473 U.S. at 676, 105. S.Ct. 3375; United States v. Agurs, 427 U.S. 97, 111-12, 96 S.Ct. 2392, 49 L.Ed.2d 342 (1976)). This is so for three reasons: McLaurin was severely impeached anyway; key parts of his testimony were corroborated by independent witnesses; and Horton’s own conduct and statements, apart from those to which McLaurin testified, were strong evidence of guilt.
Horton’s connection to the murder was established through witnesses other than McLaurin who testified that Horton asked Graham for a hammer that belonged to Dorn, Graham gave the hammer to Horton, and neither Graham nor Dorn saw the hammer again' after Graham gave it to Horton. This was in October; Dorn noticed that the hammer (which he usually kept in his office) was missing after October 11 but hadn’t seen it for about a week before that.' Horton told Dorn on the morning of October 10 that “he had something he was going to do” and that “if it worked out okay” Horton would be moving out the next day. Dorn saw Horton drive away with Doonie and Anthony about 9:30 on the morning of the murder. Bowser was killed by Dorn’s hammer, Horton left town after the crime was committed. In the next few- days Horton called Dorn a number of times asking if the police were looking for him (Horton), and Horton told Dorn to tell Graham that if anyone asked whether Graham had given anything to Horton, to deny it. All of this evidence came in. through witnesses other than McLaurin.
While McLaurin was an important witness for the prosecution, he was important primarily because he testified that Horton said and did things that were consistent with, or corroborated by, testimony from independent witnesses. For example: McLaurin testified that he drove Horton to a building on Artesia Boulevard where Horton went inside, and came out with drugs; Bowser’s girlfriend Ebel testified that Bowser sold drugs from' his apartment, which is in that building, and that Horton was. a customer whom she had seen in Bowser’s apartment. McLaurin said that Horton called his dealer a name with “Lo” in it; Ebel testified that Bowser was known as “Lobo.” McLaurin testified that Horton and Doonie and he discussed- a plan to rob Horton’s dealer the night before it happened, and that’Horton said he would not use a gun because it would be too noisy but would use a pipe; a pipe was not used, but a hammer has similar qualities. McLaurin testified that Horton said he knew his dealer kept cocaine in one of *584the kitchen cabinets; Ebel testified that Bowser kept his supply in plastic bags inside a container in a cupboard in the kitchen, that this is where Bowser’s drug deals went down, and that Horton was a customer. McLaurin testified that Horton called him about 1:00 p.m. at work and said to meet at Ray’s Motel; McLaurin’s supervisor testified that McLaurin left work, having arrived at 5:45 a.m., about 1 p.m. after receiving a telephone call. McLaurin testified that at Ray’s, Horton, Doonie and Anthony had two bags of powdered cocaine and one with cocaine rocks, and that one of the bags had black “X’s” on it; Ebel testified that Bowser kept two bags of powdered cocaine and one of rock cocaine in baggies, one of which was marked with black “X’s.” McLaurin testified that he also saw a roll of money at Ray’s; Ebel testified that catering truck money was missing from Bowser’s apartment after the murder. McLaurin testified that Horton said he clubbed Bowser in the head with a hammer, then went to the kitchen and got the cocaine; Dorn’s hammer, which Graham gave to Horton, was within a foot of Bowser’s body, the injuries to Bowser’s head were consistent with hammer blows, and Ebel as well as a police officer testified that the butter dish where Bowser kept his cocaine was uncovered and empty.
Apart from this, as the district court found, McLaurin had “credibility problems that were obvious to the jury through his own contradictory, vague, and sometimes indecipherable testimony.” McLaurin admitted to: significant drug use while he was with Horton before and after the crime; being in jail on probation violations for testing dirty; lying to the police about taking Horton to the bus depot because he was afraid he would be arrested for doing it; lying to Horton’s counsel; and never being charged with a crime in connection with the events of October 10-11. While evidence of a deal could have suggested an even stronger motive to lie, the jury knew that McLaurin participated in planning the crime, would have driven Horton to Bow-ser’s on the 10th but for his girlfriend’s intervention, and drove Horton to the bus station after the crime — -yet was neither arrested nor prosecuted. Making the inference of bias more specific would not likely have affected the total mix of information about McLaurin, which included the fact that he lied to the police about his involvement in order to avoid arrest. Nor would it likely have affected the credibility of testimony that was independently corroborated. Finally, I cannot see how evidence of a deal would have affected the weight or credibility of the evidence about Horton’s statements and conduct to which McLaurin was not percipient and about which he did not testify. Horton’s link to the murder weapon and his own behavior evincing consciousness of guilt is not affected at all by testimony adduced through McLaurin. Cf. Kyles, 514 U.S. at 441-43, 115 S.Ct. 1555 (disclosure of very different contemporaneous eyewitness statements would have substantially reduced or destroyed them trial testimony).
Horton contends that the circumstantial evidence in his case is weaker than in other cases where undisclosed deals were found material. He points in particular to Singh v. Prunty, 142 F.3d 1157, 1159 (9th Cir.1998), and Carriger v. Stewart, 132 F.3d 463, 479 (9th Cir.1997). However, these are not decisions of the United States Supreme Court, which are the decisions by which we are obliged to measure the objective reasonableness of the California court’s determination. Regardless, in Singh, the witness concerning whom the prosecution failed to disclose a deal provided the only evidence that the defendant had previously tried to hire him to commit the murder that the defendant ultimately *585hired someone else to commit; here, McLaurin’s testimony was substantially corroborated by independent evidence that connected Horton to the crime. In Carri-ger, the prosecution failed to disclose the only direct witness’s long history of lying to police and blaming his crimes on others, and compounded this failure by arguing to the jury that the witness was telling the truth about the defendant’s guilt, whereas in this case the jury heard ample evidence that McLaurin was a liar.
Horton also suggests that McLaurin himself could have been the murderer because he had a window of opportunity after he left work at 1:00 p.m. and before Ebel returned to Bowser’s apartment at 2:30 p.m., but no evidence supports any such theory. Crisp called Ebel, concerned about being unable to reach Bowser, around noon; McLaurin didn’t leave work until 1:00 p.m., which his supervisor confirmed that he did after receiving a telephone call; and there is no evidence that it would even have been possible for him to get to Bowser’s, do the deed, ransack the apartment, find the cocaine, and leave before Ebel arrived. Neither does any evidence connect McLaurin with the hammer, or manifest any consciousness of guilt except with respect to driving Horton to the bus depot.
Finally, Horton supposes that someone other than he — Cunnigan, for instance— could have provided the description of the crime to McLaurin, or that McLaurin could have learned specifics from reading the police report, which he admittedly did before testifying. That Cunnigan could have told him anything more than what McLaurin acknowledged is pure speculation; and, as the district court noted, McLaurin said . that he read the , police report before testifying at trial, but his testimony at.the preliminary hearing was consistent with his trial testimony and there is no evidence that he read the police report before testifying at that hearing.
Accordingly, I agree with the district court that the California Supreme, Court’s rejection of Horton’s Brady claim on the merits was not contrary to, or an unreasonable application of, Supreme Court law.2
. Horton submitted McLaurin's declaration to this effect to the California Supreme Court in 1995. There is no other evidence of a deal, and McLaurin testified at the preliminary hearing that he had no deal.
. Horton argues that the Brady error was compounded by the trial court's instruction that the jury must not consider why other persons than the defendant who were or may have been involved in the crime were not being prosecuted in this trial or whether they have been or will be prosecuted. Whether the instruction was erroneously given is not a certified issue on appeal. In any event, this admonition was part of an instruction that stated "[t]here has been evidence in this case indicating that persons other than defendant were or may have been involved in the crime for which the defendant is on trial." The instruction does not preclude jurors from considering involvement to the extent it bears on credibility or any thing else; it simply precludes considering why those persons are not defendants "in this trial.” Horton also relies upon juror declarations to show prejudice but, as the district court held, they are inadmissible to impeach the verdict. Fed.R.Evid. 606(b).