Washington state prisoner Michael Fur-man was tried by a death-qualified jury despite the fact that he was not subject to a potential death penalty. He also contends that he was denied a fair trial because of prosecutorial misconduct and that his trial counsel rendered ineffective assistance. His habeas petition is governed by the Antiter-rorism and Effective Death Penalty Act (“AEDPA”), 28 U.S.C. § 2254 (d). We con- elude that the Washington Court of Appeals did not act contrary to established Supreme Court precedent in ruling that Furman’s constitutional rights were not violated. See id. § 2254(d)(1).

BACKGROUND

Furman raped, robbed, and beat to death an eighty-five-year-old woman in her home. He was convicted of aggravated first degree murder and sentenced to death in Washington state court, but this sentence was vacated on direct appeal by the Washington Supreme Court on the ground that the state’s death penalty statute did not apply to minors. See State v. Furman, 122 Wash.2d 440 , 858 P.2d 1092 (1993) (en banc). Furman subsequently was sentenced to life imprisonment without the possibility of parole.

Furman filed this 28 U.S.C. § 2254 petition in district court in December 1996. He claims that he was denied due process of law because he was tried by a death-qualified jury although he was not eligible for the death penalty. He also raises claims of pros-ecutorial misconduct and ineffective assistance of counsel. The district court denied his petition and granted a certificate of ap-pealability, and Furman appeals.

DISCUSSION

1. Trial by a Death-Qualified Jury

Because this petition was filed after April 24, 1996, it is governed by 28 U.S.C. § 2254 as amended by the Antiterrorism and Effective Death Penalty Act of 1996, Pub.L. No. 104-132, 110 Stat. 1214. See Lindh v. Murphy, 521 U.S. 320, 336-38 , 117 S.Ct. 2059, 2068 , 138 L.Ed.2d 481 (1997). The Washington Court of Appeals rejected Fur-man’s claim that his trial by a death-qualified jury violated the Fourteenth Amendment’s due process guarantee. We will disturb this decision only if it was “contrary to, or 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).

We previously have determined that the standard of “unreasonable application of[ ] clearly established Federal law” in the new § 2254 governs mixed questions of law and fact, while the standard of “contrary to ... clearly established Federal law” applies to pure questions of law. See Moore v. Calderon, 108 F.3d 261 , 265 n. 3 (9th Cir.1997). Furman argues that federal law requires that the state have a compelling interest if it is to try by a death-qualified jury an individual who is not eligible for the death penalty. Because this contention raises a purely legal issue, our inquiry is whether the state court’s decision was “contrary to ... clearly established Federal law.”

The amended statute places an additional constraint on our review of state criminal proceedings. For the writ to issue, Fur-man’s conviction must be contrary to clearly established federal law, “as determined by the Supreme Court of the United States,” § 2254(d)(1) (emphasis added). As we have previously explained,

Moore, 108 F.3d at 264 . Thus, “we are no longer permitted to apply our own jurisprudence, but must look exclusively to Supreme Court caselaw in reviewing” Furman’s claim. Sweeney v. Parke, 113 F.3d 716, 718 (7th Cir.1997). The many court of appeals decisions relied on by Furman are irrelevant to our analysis. See Devin v. DeTella, 101 F.3d 1206 , 1209 n. 2 (7th Cir.1996) (“the lower court decisions cited by petitioner cannot carry the day”). Furman cites two United States Supreme Court decisions that address the death qualification of juries: Lockhart v. McCree, 476 U.S. 162 , 106 S.Ct. 1758 , 90 L.Ed.2d 137 (1986), and Buchanan v. Kentucky, 483 U.S. 402 , 107 S.Ct. 2906 , 97 L.Ed.2d 336 (1987). Our inquiry is centered on these eases.

McCree holds that death qualification does not deny the capital defendant a fair guilt phase trial. The Court.found no support for the proposition that death qualification produces a jury that is conviction-prone. See McCree, 476 U.S. at 168-173 , 106 S.Ct. 1758 . Indeed, to the extent that attitudes toward the death penalty influence deliberations, the Court found greater cause for concern in the prospect that jurors who are hostile to the death penalty may be acquittal-prone. See id. at 172 , 106 S.Ct. 1758 . Furthermore, the Court ruled that, even if it is assumed that death qualified jurors are conviction-prone, the presence on the jury of jurors who are opposed to the death penalty is not protected by the fair-eross-seetion requirement. See id. at 174-77 , 106 S.Ct. 1758 .

Finally, the Court rejected the argument that death qualification denies the defendant an impartial jury. It again assumed that death qualification affects certain deliberations, noting that it had invalidated sentencing schemes that remove all jurors who express any scruples against the death penalty in Witherspoon v. Illinois, 391 U.S. 510 , 88 S.Ct. 1770 , 20 L.Ed.2d 776 (1968), and Adams v. Texas, 448 U.S. 38 , 100 S.Ct. 2521 , 65 L.Ed.2d 581 (1980). The Court distinguished those cases on the basis that the constitutional error in those cases affected only the penalty phase, but not the guilt phase, where the jury’s discretion is more closely channeled. See id. at 183 , 106 S.Ct. 1758 .

Buchanan tracks McCree’s analysis. It holds that death qualification does not violate the rights of a non-capital defendant tried jointly with a capital defendant. The Court again rejected a fair-cross-section challenge to death qualification, see Buchanan, 483 U.S. at 416 , 107 S.Ct. 2906 . And the Court rejected a partiality argument, noting that McCree had found that to the extent that death qualification affects deliberations, it does so at the penalty phase, not at the guilt phase, where jury discretion is closely channeled. Death qualification therefore does not affect the rights of a non-capital defendant. See id. at 420, 107 S.Ct. 2906 .

Buchanan did point out that the state has a legitimate interest in trying some defendants jointly. See id. at 418-19 , 107 S.Ct. 2906 . Furman contends that it was only because of this interest that death qualification was allowed in that case for the non-capital defendant. The Supreme Court, however, did not make this point a basis for its decision in Buchanan . It simply indicated that the state had reasons for trying the defendants jointly. Furman would read into this a rule by negative implication that trial of a non-capital defendant by a death-qualified jury requires a compelling state interest. This negative implication, however, hardly qualifies as “clearly established” law within the meaning of 28 U.S.C. § 2254 (d)(1). Because the Washington Supreme Court’s rejection of Furman’s death qualification claim is not contrary to clearly established Supreme Court precedent, we may not disturb its judgment.

2. Remaining Issues-Certificate of Ap-pealability

Before addressing the additional issues raised by Furman, we face a threshold question. The State argues that the Certificate of Appealability was granted only as to Furman’s death qualification claim, not his prosecutorial misconduct and ineffective assistance claims. The district court’s order states, “For the reasons set forth in the Magistrate Judge’s Report and Recommendation ..., the petitioner has made a substantial showing of the denial of a constitutional right, particularly the issue of death qualification of the jury when he was not eligible for the death penalty.”

Although the district court’s order emphasizes the death qualification claim, it does not purport to exclude the other claims. The referenced Magistrate’s report addresses all three claims. We construe .the district court’s certificate liberally and find that all three issues were certified. We thus reach the merits of Furman’s prosecutorial misconduct and ineffective assistance claims, without the necessity of Furman’s moving to have us certify them. See Ninth Circuit Rule 22-1; see also United States v. Cruz-Mendoza, 163 F.3d 1149 , amending 147 F.3d 1069 (9th Cir.1998).

3. Prosecutorial Misconduct

Furman argues that several comments of the prosecutor amounted to prose-cutorial misconduct that deprived him of the right to a fair trial. He points to several instances in the record: (1) the prosecutor during opening statement made repeated inferences to “twisted, and ugly, and vicious” conduct of the defendant, despite repeated objections that were sustained; (2) the prosecutor inquired whether Furman had been a hyperactive child, suggesting that amphetamines have a reverse effect on such children (thus discrediting Furman’s contention that he was too intoxicated by “speed” to premeditate); (3) the prosecutor asked Furman whether, during the 100 times he had taken “speed,” this was the only time he had killed anyone; and (4) the prosecutor referred to Furman as a “con artist.”

The Washington Supreme Court rejected Furman’s prosecutorial misconduct claim:

This issue, too, is governed by the amendments to 28 U.S.C. § 2254 effected by the Antiteirorism and Effective Death Penalty Act of 1996. There being no dispute as to the relevant legal standard, the Washington Supreme Couxi’s conclusion will be disturbed only if it is an unreasonable application of Supreme Court precedent, 28 U.S.C. § 2254 (d)(1), or is based on an unreasonable determination of the facts as presented in the state coxxrt proceedings, id. § 2254(d)(2).

Many of the prosecutor’s comments were improper, and the prosecutor persisted in some of them despite several objections that were sustained. Prosecutorial misconduct, however', does not automatically invalidate a conviction. It is a ground for relief if it “so infected the trial with unfairness as to make the resultant conviction a denial of due process.” Darden v. Wainwright, 477 U.S. 168, 181 , 106 S.Ct. 2464 , 91 L.Ed.2d 144 (1986). In determining that question, it is appropriate to consider whether the jury was instructed to decide solely on the basis of the evidence rather than counsel’s arguments, and whether the state’s case was strong. See id. at 182 , 106 S.Ct. 2464 .

See also id. (“several neighbors who saw [Furman] shortly before the murder noticed no [drug] impairment, and he admitted in his confession that he killed the victim because he did not want her to be a witness.”)

In this case the jury was told by the prosecutor himself that his arguments are not evidence. The Washington Supreme Court’s finding that the evidence of premeditation was strong is not unreasonable. We thus decline to disturb its conclusion that the prosecutor’s occasional but perseverant indiscretions did not so prejudice the jury as to deny Furman due process.

4. Ineffective Assistance of Counsel

To buttress his claim that he was too intoxicated on the day of the murder to be held accountable for his behavior, Furman called a psychological expert who testified that drugs had rendered him unable “to reflect, or consider or deliberate! ] about the mechanics of his actions.” The expert also testified that Furman had told him that up to the day of the murder he had been smoking half an ounce, or $80 worth, of crystal a day.

A prosecution expert then testified that half an ounce of “speed” would cost between $500 and $1000, and that half a gram would cost $80. Another prosecution expert testified that smoking half an ounce of speed a day would certainly kill a person. In response, the defense called another witness who testified that it is possible for a person to smoke half an ounce of speed a day. The defense did not otherwise allude to the issue of the amount of speed Furman smoked. In closing arguments, the prosecutor contended that it was extremely unlikely that Furman was smoking half an ounce a day, and argued that Furman acted deliberately on the day of the murder.

Furman now contends that he was denied effective assistance of counsel by his counsel’s failure to clarify to the jury that his expert simply had misnoted that Furman smoked half an ounce, rather than half a gram, of speed a day. Furman argues that this error injured his credibility and undermined his defense.

The Washington Court of Appeals rejected this claim. First it found that Furman was not prejudiced, because

Second, it found that defense counsel’s decision not to return to the issue of the amount of speed was tactical. It quoted counsel’s averment that:

Relief will be granted if counsel’s performance fell outside a wide range of reasonableness 'and defendant was prejudiced. Strickland v. Washington, 466 U.S. 668, 687, 694 , 104 S.Ct. 2052 , 80 L.Ed.2d 674 (1984). Counsel’s tactical decisions are “virtually unchallengeable.” Id. at 690 , 104 S.Ct. 2052 .

The state court’s conclusion that Furman was not prejudiced by his attorney’s failure to return to the ounce issue, because the jury must have understood that a mistake as to amount had been made, is not unreasonable. See 28 U.S.C. § 2254 (d). Its conclusion that the attorney’s decision was tactical also is reasonable. See id. Because the Washington Supreme Court’s applications of Strickland were reasonable, we are barred from granting relief on Furman’s petition. See id. § 2254(d)(1).

CONCLUSION

The judgment of the district court is

AFFIRMED.

. That is, a jury from which prospective jurors who are biased against the death penalty have been excluded. . Furman makes a passing reference to other alleged instances of misconduct, but does not explain how they are misconduct and it is not clear that they could be so or are other than trivial.