Opinion by Judge TASHIMA; Dissent by Judge BRIGHT.

For the second time, Charles Murdoch, a California state prisoner, appeals from the judgment of the district court denying his petition for a writ of habeas corpus. In his previous appeal, we held that the exclusion of a privileged letter could violate a defendant’s Sixth Amendment right to confrontation and cross-examination, depending on the content of the letter. Murdoch v. Castro, 365 F.3d 699, 705 (9th Cir.2004) (“Murdoch I”). We therefore remanded for the district court to review the letter and to determine whether the attorney-client privilege must yield to the petitioner’s right of cross-examination. Id. at 706 . On remand, after reviewing the letter, the district court held that there was no constitutional violation. We have jurisdiction pursuant to 28 U.S.C. § 2253 , and we affirm.

I. BACKGROUND

On May 17, 1983, four men robbed the Horseshoe Bar in Long Beach, California. In the course of the robbery, one bystander was shot and killed; another was stabbed and severely wounded. The men recovered approximately $200 from the cash register and left behind a fingerprint. The crime went unsolved until 11 years later, when advances in fingerprint technology enabled police to identify Dino Dinardo as one of the perpetrators.

Officers arrested Dinardo on June 30, 1994, in Berkeley, California. When first questioned, Dinardo denied any involvement in the crime, but later recanted, admitting his involvement in the robbery, and identifying Murdoch as one of his accomplices. Both Dinardo and Murdoch were charged with murder accompanied by special circumstances.

Dinardo was tried first. At a suppression hearing that preceded his trial, Dinar- *1065 do testified that his confession to the Long Beach police had been coerced, and that he had given the confession in exchange for a promise that he would be released to see his wife and daughter. Dinardo was convicted and was sentenced to 25 years’ to life imprisonment. At sentencing, the judge suggested to Dinardo that his sentence could be reduced were he to testify against Murdoch. Dinardo agreed and received in return a reduction of his conviction to voluntary manslaughter and a reduced sentence of 12 years’ imprisonment.

Dinardo was a key witness at Murdoch’s trial. He testified that, in 1983, Murdoch had approached him “to do a job” and that the two of them, together with two other men, robbed the Horseshoe Bar. According to Dinardo, when they entered the bar, Murdoch carried a .22 caliber rifle and announced loudly, “Don’t nobody move. This is a stick-up.” Dinardo took this as his cue to empty the cash register. He fumbled with the buttons on the register, heard a gunshot, emptied the register, and ran out the back door, joining the other two men in the getaway car, with Murdoch joining them about a minute later. He recalled seeing Murdoch in possession of the rifle both in the bar and in the car. Dinardo testified that the first time he learned that someone had been shot in the robbery was the day of his arrest, 11 years after the crime.

During Murdoch’s trial, Murdoch’s attorney, Dinardo’s attorney, the prosecutor, and the presiding judge discussed a letter addressed to Dinardo’s former counsel. The letter was first brought to the court’s attention by the prosecutor, who indicated that in her interviews of Dinardo, he told her of the existence of a letter in which he, Dinardo, stated that he was coerced by the police into implicating Murdoch in the crime. Dinardo’s new counsel asserted the attorney-client privilege and work-product doctrine as grounds for refusing to disclose the letter. The court concluded that Dinardo’s letter to his former counsel was protected by the attorney-client privilege and thus could not be used, on cross-examination, to impeach Dinardo.

Although Dinardo was not cross-examined about the letter, Murdoch’s counsel succeeded in eliciting testimony that challenged Dinardo’s credibility as a witness. Dinardo testified that he had been convicted of the same murder for which Murdoch was now being tried and that by testifying in Murdoch’s trial, he would “get out in about five years” rather than 21 or more years. He admitted that when he was initially questioned by the police, he had lied and denied that he had ever been inside the Horseshoe Bar. He admitted that he would have done “whatever it took” to get out of custody and be reunited with his daughter. He also testified to convictions for grand theft in 1982 and petty theft in 1984. On re-direct examination by the prosecutor, Dinardo testified that during the police questioning, he named a “Charles or Chuck” as someone else involved in the crime, but he could not remember the last name. He was shown photographs at the end of the interview, and he identified Murdoch as one of his accomplices. On re-cross, he stated that he had testified in his own trial that his confession had been coerced. He also admitted that, had the fingerprints not identified him as one of the robbers, he would have continued to lie to the police about his involvement.

In addition to Dinardo, other witnesses from the Horeshoe Bar testified and provided in-court identification of Murdoch. The bartender, Dyanne Spence, described looking into Murdoch’s eyes down the barrel of a rifle pointed at her face. “He’s been scaring me for years,” she said. She also testified that she had identified Mur *1066 doch at a live lineup at the county jail in 1994 and that she was sure “beyond a shadow of a doubt” that Murdoch had committed the crime.

Murdoch was convicted of first-degree murder with a robbery-murder special circumstance, and sentenced to life imprisonment without parole. The California Court of Appeal affirmed the conviction, and denied Murdoch’s petition for a writ of habeas corpus. The California Supreme Court denied Murdoch’s petition for review.

Murdoch then filed a federal petition for a writ of habeas corpus, which the district court dismissed. On appeal, we vacated the order denying Murdoch’s habeas petition and remanded the case to the district court stating:

Murdoch I, 365 F.3d at 702 . We concluded that if the contents of Dinardo’s letter “are as generally described by the prosecutor and as Murdoch believes,” then Murdoch “has arguably met his burden” of showing that the jury might have received a significantly different impression of the witness’ credibility had Murdoch been able to pursue his proposed line of cross examination. Id. at 705 . General impeachment for bias implicated Dinardo’s reliability to a lesser extent than actual statements inconsistent with his testimony, such as those which the letter purportedly contained. Id. Without knowing the contents of the letter, however, we could not make a determination of whether Murdoch’s confrontation rights had been violated. We accordingly remanded the case to the district court with instructions that the court obtain the letter, inspect it in camera, and determine whether the state court’s decision to deny Murdoch access to the letter violated Murdoch’s Sixth Amendment right of confrontation. Id. at 706 .

On remand, the magistrate judge, in his report and recommendation, began from the premise that “[essentially, the Ninth Circuit held that the attorney-client privilege might have to yield in a particular case if the right of confrontation would be violated by enforcing the privilege.” The report addressed four issues: (1) whether the contents of the letter were examined by the state courts during the petitioner’s postconviction proceedings; (2) whether the state courts weighed the probative value of the letter and petitioner’s right to confront witnesses against Dinardo’s attorney-client privilege; (3) whether weighing the rights at stake would indicate a constitutional violation; and, if so, (4) whether the violation represented harmless error.

Regarding the first two issues, the magistrate judge concluded that although the state courts had read the contents of the letter, their decisions were “contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States,” within the meaning of 28 U.S.C. § 2254 (d)(1), in that they failed to perform any balancing of Murdoch’s Sixth Amendment rights against the privilege.

The report next examined the contents of the letter to determine whether a constitutional violation had occurred. It concluded that the letter’s intrinsic probative value was low, given that of the four factual assertions in the letter, “trial testimony rebutted the first three, and half of the *1067 fourth.” This observation segued into a discussion of Murdoch’s rights to cross-examine, which in turn relied on an analysis of the probative value of the letter. The magistrate judge summarized the contents of the letter as asserting the following facts: (1) After Dinardo’s arrest in Berkeley, Long Beach Police Detective Pa-vek coerced a statement from Dinardo by promising not to charge Dinardo in exchange for Dinardo’s statement; (2) In his statement, Dinardo was forced to identify petitioner Murdoch as a participant in the crime; (3) Dinardo does not actually know Murdoch, although Dinardo is acquainted with Murdoch’s brother; and (4) Murdoch and Dinardo did not commit any crime.

The magistrate judge then summarized trial testimony that rebutted these factual assertions. Because the factual assertions in the letter had been “contradicted by trial testimony” or “were demonstrably false in the light of other testimony,” the “intrinsic probative value of the letter was and is low.” Thus, the exclusion of the letter from evidence did not substantially diminish Murdoch’s right to effective cross-examination. The magistrate judge also concluded that the decision to exclude the letter was subject to harmless error analysis, and, further concluded, under the Brecht v. Abrahamson standard, 507 U.S. 619, 637 , 113 S.Ct. 1710 , 123 L.Ed.2d 353 (1993), that there was no “grave doubt” as to whether the jury would have reached a different result had the letter been admitted. While acknowledging that “Dinardo’s testimony was crucial,” the magistrate found that “Dinardo’s prior inconsistent statement was inextricably linked with other statements which either conflicted with other evidence or were demonstrably false.” Therefore, he concluded that any error resulting from the exclusion of the letter was harmless.

The district court adopted the findings and recommendation of the magistrate judge and denied Murdoch’s habeas petition. Murdoch filed a timely notice of appeal. We granted a certificate of ap-pealability on the issue of “whether the district court erred by ruling that the state trial court did not violate the Sixth Amendment right to confrontation when it denied him access to Dinardo’s letter.”

II. STANDARD OF REVIEW

We review de novo the district court’s denial of a § 2254 habeas petition. Insyx-iengmay v. Morgan, 403 F.3d 657, 665 (9th Cir.2005). Under the Antiterrorism and Effective Death Penalty Act of 1996, a habeas petition challenging a state court conviction will not be granted unless the decision “was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States.” 28 U.S.C. § 2254 (d)(1).

III. DISCUSSION

As noted, this is the second time we have examined whether California’s attorney-client privilege bars Murdoch from seeing or using an exculpatory letter written by the state’s witness to his lawyer. The starting point of our analysis is thus the law-of-the-case doctrine, which “ ‘posits that when a court decides upon a rule of law, that decision should continue to govern the same issues in subsequent stages in the same case.’ ” Christianson v. Colt Indus. Operating Corp., 486 U.S. 800, 816 , 108 S.Ct. 2166 , 100 L.Ed.2d 811 (1988) (quoting Arizona v. California, 460 U.S. 605, 618 , 103 S.Ct. 1382 , 75 L.Ed.2d 318 (1983)). “This rule of practice promotes the finality and efficiency of the judicial process by ‘protecting against the agitation of settled issues.’ ” Id. (quoting IB J. Moore, J. Lucas, & T. Currier, Moore’s *1068 Federal Practice 118 (1984)). “For the doctrine to apply, the issue in question must have been ‘decided explicitly or by necessary implication in [the] previous disposition.’ ” Milgard Tempering v. Selas Corp. of Am., 902 F.2d 703, 715 (9th Cir.1990) (quoting Liberty Mutual Ins. Co. v. EEOC, 691 F.2d 438, 441 (9th Cir.1982)) (alteration in original). 1

In Murdoch’s prior appeal, we held that, under the right set of facts, Supreme Court precedent suggests the Sixth Amendment right to confrontation could support admission of the letter, even against a valid claim of attorney-client privilege. Murdoch I, 365 F.3d at 706 . We vacated the district court’s denial of Murdoch’s habeas petition and remanded the case with instructions that the district court review the letter in camera to determine “whether, as applied to the totality of facts in this case, the denial of access to Dinardo’s letter resulted in an unconstitutional denial of Murdoch’s Sixth Amendment right to confront witnesses.” Id. A necessary implication of our decision — and hence, law of the case — is that the confrontation clause could support introduction of the letter as evidence. Otherwise, there would have been no ground upon which to vacate the decision of the district court. 2

We therefore proceed to the question of whether Murdoch’s Sixth Amendment rights were violated by the exclusion of the privileged letter. 3 The Sixth Amendment guarantees Murdoch the right “to be confronted with the witnesses against him.” U.S. Const. Amend. VI. “Confrontation means more than being allowed to confront the witness physically. ‘Our cases construing the (confrontation) clause hold that a primary interest secured by it is the right of cross-examination.’ ” Davis v. Alaska, 415 U.S. 308, 315 , 94 S.Ct. 1105 , 39 L.Ed.2d 347 (1974) (quoting Douglas v. Alabama, 380 U.S. 415, 418 , 85 S.Ct. 1074 , 13 L.Ed.2d 934 (1965)).

Although Murdoch’s attorney cross-examined and recross-examined Dinardo, this alone does not resolve whether Murdoch was afforded his right to cross-examination, because “the Confrontation Clause requires that a defendant be given an opportunity for effective cross-examination.” Murdoch I, 365 F.3d at 704 (emphasis added). Effectiveness requires that “the trier of fact [have] a satisfactory basis for evaluating the truth of the prior statement.” California v. Green, 399 U.S. 149, 161 , 90 S.Ct. 1930 , 26 L.Ed.2d 489 (1970). “When exploring the credibility of a prosecution witness who testifies against a criminal defendant, it is axiomatic that the *1069 defendant may employ the witness’s prior inconsistent statements in order to impeach the credibility of the witness.” United States v. Adamson, 291 F.3d 606, 612 (2002). “ “Wide latitude in cross-examination is especially appropriate when the key witness is an accomplice of the accused.’ ” Murdoch I, 365 F.3d at 704 (quoting Burr v. Sullivan, 618 F.2d 583, 587 (9th Cir.1980)); see also United States v. Mayans, 17 F.3d 1174, 1184 (9th Cir.1994) (the right to cross-examination is “ ‘especially important with respect to accomplices or other witnesses who may have substantial reason to cooperate with the government’ ”) (quoting United States v. Onoti, 535 F.2d 938, 945 (5th Cir.1976)).

Here, Murdoch’s counsel was able, by effective cross-examination, to raise doubts as to Dinardo’s biases and motivations. Dinardo testified that his sentence was reduced to “about five years” in exchange for his testimony. He testified about his previous theft convictions, both before and after the robbery in question. He testified to prior inconsistent statements: that at the time of his arrest he initially denied any involvement in the crime; that he “would have said whatever it took to get out of custody” including “pointfing] out someone else” involved in the crime; that he pleaded “not guilty” at his own trial and “avoid[ed] responsibility” for the crime; and that his story had changed from earlier claims that the police had coerced his confession. Dinardo equivocated on the stand when confronted with prior inconsistent testimony: “I testified to that? ... I — I can’t remember testifying like that. If I could see it, I could probably remember.” In sum, Dinardo’s cross-examinations were effective.

The confrontation clause “guarantees only ‘an opportunity for effective cross-examination, not cross-examination that is effective in whatever way, and to whatever extent, the defense might wish.’ ” United States v. Owens, 484 U.S. 554, 559 , 108 S.Ct. 838 , 98 L.Ed.2d 951 (1988) (quoting Kentucky v. Stincer, 482 U.S. 730, 739 , 107 S.Ct. 2658 , 96 L.Ed.2d 631 (1987)). “ ‘A limitation on cross examination does not violate the Confrontation Clause unless it limits relevant testimony and prejudices the defendant, and denies the jury sufficient information to appraise the biases and motivations of the witness.’ ” United States v. Bridgeforth, 441 F.3d 864, 868 (9th Cir.2006) (quoting United States v. Holler, 411 F.3d 1061, 1066 (9th Cir.2005)). We conclude that here the jury was provided ample information on which to measure Dinardo’s biases, particularly given his admission that he earlier denied any involvement on his or Murdoch’s part in the crime.

Although we can imagine a letter of such probative value that its exclusion would render cross-examination constitutionally defective, Dinardo’s letter is not such a letter. We agree with the reasoned analysis of the magistrate judge that the letter is of low probative value. The assertions in the letter run contrary to the testimony of Murdoch’s brother, his former roommate, the investigating detective, the eyewitnesses at the crime, and the fingerprints at the crime scene. Although questioning about the letter may have added some marginal benefit to Murdoch’s cross-examination, its absence did not deny the jury sufficient information to appraise the biases and motivations of the witness.

In light of the low probative value of the letter and the otherwise effective cross-examination, we hold that Murdoch’s constitutional right to confrontation did not require the disclosure of Dinardo’s letter *1070 to Murdoch’s counsel. 4 Accordingly, the district court’s denial of Murdoch’s petition for a writ of habeas corpus is AFFIRMED.

. No party contends that the law of the case does not apply. Thus, we need not inquire whether any exception to that doctrine should apply. See United States v. Lummi Indian Tribe, 235 F.3d 443, 452-53 (9th Cir.2000) (enumerating the exceptions to the doctrine).

. Also necessarily implicit in our decision in Murdoch I was that Supreme Court precedent had "clearly established,” as required by 28 U.S.C. § 2254 (d)(1), that under the proper circumstances, shielding a witness’ letter to his attorney under the attorney-client privilege could violate a defendant's confrontation rights under the Sixth Amendment. We note that other circuits have arrived at the same conclusion as Murdoch I that, under Supreme Court precedent, the attorney-client privilege must sometimes yield to the Sixth Amendment right to confrontation. See Mills v. Singletary, 161 F.3d 1273 (11th Cir.1998); United States v. Rainone, 32 F.3d 1203, 1206 (7th Cir.1994).

. Like the panel before us, we are bound by the state court's interpretation of its evidence law — that Dinardo’s letter is protected by the attorney-client privilege. Murdoch I, 365 F.3d at 703 n. 1 (quoting Jammal v. Van de Kamp, 926 F.2d 918, 919 (9th Cir.1991) ("We are not a state supreme court of errors; we do not review questions of state evidence law.”)).

. Because we hold that Murdoch's Sixth Amendment rights were not violated, we need not reach the issue of whether a violation would have constituted harmless error under Brecht, 507 U.S. at 637 , 113 S.Ct. 1710 .