
603 F.3d 1127 (2010)
Johnny Paul COLLINS, Petitioner-Appellant,
v.
D.L. RUNNELS, Warden; Attorney GGH General of the State of California, Respondents-Appellees.
No. 08-17299.
United States Court of Appeals, Ninth Circuit.
Argued and Submitted January 13, 2010.
Filed May 5, 2010.
*1128 Fay Arfa, Los Angeles, CA, for the appellant.
David Andrew Eldridge and Justain Riley, Deputy Attorneys General, Sacramento, CA, for the appellees.
Before: ALEX KOZINSKI, Chief Judge, PROCTER HUG, JR. and RICHARD R. CLIFTON, Circuit Judges.
HUG, Circuit Judge:
Johnny Paul Collins appeals the district court's denial of his 28 U.S.C. § 2254 habeas corpus petition challenging his jury conviction of first degree murder and second degree robbery. Collins was sentenced to life without the possibility of parole in a California state court. The central issue on appeal is whether clearly established Supreme Court precedent binding on the states requires trial severance where a co-defendant presents a mutually antagonistic defense. We hold that the cases upon which Collins relies for this argument do not bind the states, so the decision of the California Court of Appeal was not contrary to or an unreasonable application of clearly established federal law as determined by the Supreme Court. Accordingly, *1129 we affirm the district court's denial of the writ of habeas corpus.

I. FACTUAL AND PROCEDURAL BACKGROUND
On October 22, 1998, Robert Yee and his wife, Sim Yee, were robbed while closing their convenience market in Rio Linda, California. They were forced to lie down after which their hands and feet were tied and duct tape was placed over their mouths. Mr. Yee was kicked and hit on the head with a heavy object, but nevertheless managed to free himself and summon help. Mrs. Yee, who suffered from impaired lungs and an enlarged heart, died.
Investigators identified Collins, Shaun Anderson, and James M. as the suspected robbers. James M. confessed to the robbery and agreed to testify against his co-defendants in exchange for a deal permitting him to plead guilty to murder as a juvenile. Collins and Anderson were jointly charged with robbery and first degree murder. Before trial, it became evident that they intended to present mutually antagonistic defenses. Collins planned to present an alibi defense attempting to show that he was on the telephone with his brother at the time of the robbery. Anderson intended to present a duress defense claiming that Collins had coerced him and James M. into participating in the robbery. Collins moved to have his case severed from that against Anderson, arguing that a jury might infer that if Collins coerced Anderson into committing the robbery, Collins must also have been part of the robbery, thus contradicting his alibi defense. Collins also argued that Anderson's planned testimony regarding their prior joint criminal activities and Collins' alleged coercion of Anderson would cause the jury to become unduly prejudiced against Collins and thus more likely to find him guilty. According to Collins, this situation would deprive him of his constitutional rights to due process and a fair trial. The trial court recognized the existence of some antagonism, but found that the defenses were not so antagonistic as to render a joint trial inherently unfair to Collins. In so finding, the trial court emphasized the California Legislature's preference for joint trials and the policy considerations favoring one jury hearing all issues and finding all facts at one time.
At trial, several witnesses were called. These included James M., who confessed to participating with Collins in the planning and execution of the robbery, and Vanessa H., who also presented strong testimony incriminating Collins. Anderson testified on his own behalf, corroborating James M.'s testimony regarding Collins' involvement in the robbery and asserting his own duress defense. Nonetheless, Collins presented an alibi defense. At the conclusion of the trial, the court instructed the jury to consider Anderson's testimony regarding Collins' prior coercion only as to Anderson's state of mind. The court also excluded evidence regarding the defendants' prior joint criminal acts. The jury found Collins guilty of robbery and murder, but deadlocked on the identical charges against Anderson.[1]
Collins subsequently moved for a new trial based on the failure to sever. The trial court rejected the motion, reiterating its previous arguments and adding that the significant amount of evidence against Collins created a compelling case against him even absent Anderson's testimony. The trial court concluded that Collins could not have overcome these obstacles even if a separate trial had been granted.
Collins appealed his conviction to the California Court of Appeal, again asserting *1130 that the joint trial was unduly prejudicial. The Court of Appeal held that neither California nor federal law required trial severance under the circumstances and that Collins' due process rights had not been violated. It explained that Collins had been able to confront Anderson's conflicting evidence, which would have been admissible even if a separate trial had been granted. It further explained that there was no indication that the joint trial induced the jury to convict Collins without proof beyond a reasonable doubt. It also noted that the jury deadlocked against Anderson, demonstrating that the jury had considered the charges against the defendants separately. The Court of Appeal held that even if the trial court's refusal to order separate trails was error, any error was harmless because of the overwhelming evidence against Collins. Accordingly, the Court of Appeal affirmed Collins' conviction. The California Supreme Court summarily denied review of that decision as well as of Collins' writ of habeas corpus repeating his prejudice arguments.
Subsequently, Collins filed a petition for a writ of habeas corpus pursuant to 28 U.S.C. § 2254 with the United States District Court for the Eastern District of California, once again presenting his prejudice and severance arguments. The District Court adopted the recommendation of a magistrate judge that Collins' petition be denied, finding that no clearly established federal law binding on the states requires severance of co-defendants' trial when they present mutually antagonistic defenses. The district court issued a Certificate of Appealability under 28 U.S.C. § 2253(c) and Federal Rule 22(b) of Appellate Procedure. This appeal followed. We have jurisdiction pursuant to 28 U.S.C. § 2253.

II. STANDARD OF REVIEW
We review de novo a district court's decision to grant or deny a habeas corpus petition under 28 U.S.C. § 2254. Yee v. Duncan, 463 F.3d 893, 897 (9th Cir.2006).
Because Collins filed his habeas petition after the effective date of the Anti-Terrorism and Effective Death Penalty Act ("AEDPA"), that statute's provisions apply and pose special requirements. Chein v. Shumsky, 373 F.3d 978, 983 (9th Cir.2004) (en banc). Under AEDPA, we can grant relief only if the state court's adjudication of the merits of the case "(1) resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States; or (2) resulted in a decision that was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding." 28 U.S.C. § 2254(d)(1)-(2). State court findings of fact are presumed to be correct unless the petitioner rebuts that presumption with clear and convincing evidence. 28 U.S.C. § 2254(e)(1); Davis v. Woodford, 333 F.3d 982, 991 (9th Cir.2003). In applying these standards of review, we look to the "last reasoned decision" in the state court system; here, the opinion of the California Court of Appeal. Yee, 463 F.3d at 897.

III. ANALYSIS
In California, "[w]hen two or more defendants are jointly charged with any public offense, whether felony or misdemeanor, they must be tried jointly." Cal. Pen.Code § 1098. The trial court may, however, order separate trials in its discretion. Id. The denial of a motion to sever is, in California, reviewed for an abuse of discretion and analyzed on the basis of the facts as they appear at the time of the hearing on the motion to sever. People v. Boyde, 46 Cal.3d 212, 250 Cal.Rptr. 83, 758 P.2d 25, 34 (1988).
*1131 The California Court of Appeal held that the trial court did not abuse its discretion in denying Collins' motion for severance or a new trial based on the existence of Anderson's mutually antagonistic defense.[2] In analyzing whether the trial court should have severed the cases against Collins and Anderson, the Court of Appeal looked to California law discussing antagonistic defenses, but finding that jurisprudence scant, the Court of Appeal also used United States Supreme Court precedent as an aid in interpreting California's procedural rules and preferences for joint trials. In particular, the Court of Appeal relied on Zafiro v. United States, 506 U.S. 534, 113 S.Ct. 933, 122 L.Ed.2d 317 (1993), in finding that neither state or federal law required trial severance. Collins argues that the state court's conclusion runs afoul of the holdings in both Zafiro and United States v. Lane, 474 U.S. 438, 106 S.Ct. 725, 88 L.Ed.2d 814 (1986). Collins contends that these cases establish a constitutional standard binding on the states and require severance in cases where defendants present mutually antagonistic defenses. We hold that they do not.
In Zafiro, the four petitioners were indicted on federal drug charges and brought to trial together pursuant to Federal Rule of Criminal Procedure 8(b). 506 U.S. at 535-36, 113 S.Ct. 933. On appeal, petitioners invoked Federal Rule of Criminal Procedure 14, which at the time provided that "[i]f it appears that a defendant or the government is prejudiced by a joinder of ... defendants(3)27for trial together, the court may order an election or separate trials of counts, grant a severance of defendants, or provide whatever other relief justice requires." Id. at 538, 113 S.Ct. 933.[3] Petitioners argued that this language mandates severance whenever codefendants present conflicting defenses. Id. at 538, 113 S.Ct. 933. The Court declined adopting such a bright-line rule, holding that mutually antagonistic defenses are not prejudicial per se. Id. Moreover, the Court concluded that Rule 14 does not require severance even if prejudice is shown. Id. at 538-39, 113 S.Ct. 933 (emphasis added). "[R]ather, it leaves the tailoring of the relief to be granted, if any, to the district court's sound discretion." Id. at 539, 113 S.Ct. 933. "[L]ess drastic measures, such as limiting instructions, often will suffice to cure any risk of prejudice." Id.
First, Collins argues that Zafiro is binding on state courts. It is not. By its own *1132 wording, Zafiro only applies to federal and not state court trials. It analyzes only the Federal Rules of Criminal Procedure applicable to federal district courts. Collins's argument thus fails. The California Court of Appeal did not violate clearly established federal law in refusing to find that separate trials should have been granted here merely because of the existence of antagonistic defenses.
Even if Zafiro did apply to Collins' case, it would not require severance on the ground that Anderson's defense made it more difficult for Collins to argue his innocence, as Collins also argues. "[I]t is well settled that defendants are not entitled to severance merely because they may have a better chance of acquittal in separate trials." Id. at 540, 113 S.Ct. 933.
Further, both Collins and the Court of Appeal cite to Zafiro's language discussing whether severance should be granted when "there is a serious risk that a joint trial would compromise a specific trial right of one of the defendants, or prevent the jury from making a reliable judgment about guilt or innocence." Id. at 539, 113 S.Ct. 933. Even if this language were applicable to Collins' state court case, Zafiro's illustrations of when such a serious risk might arise are inapposite to Collins' case. The Supreme Court stated that this risk might, for example, be a concern in complex cases where defendants have markedly different degrees of culpability, cases where evidence is probative of a defendant's guilt, but technically only admissible against a codefendant, and cases where essential exculpatory evidence that would be available to one defendant if tried alone is unavailable in a joint trial. Id. None of these situations were a concern in Collins' case.
Collins also argues that under Lane, misjoinder rises to the level of a constitutional violation "if it results in prejudice so great as to deny a defendant his Fifth Amendment right to a fair trial." Lane, 474 U.S. at 446 n. 8, 106 S.Ct. 725. According to Collins, the prejudice rose to that level in his case because Anderson's defense had a substantial and highly injurious effect on the jury in determining its verdict.
The language upon which Collins refers is dicta. Lane dealt with the joinder of standards under Federal Rules of Criminal Procedure 8 and 52; no constitutional issue was before the Court. "[T]he phrase `clearly established Federal law, as determined by the Supreme Court of the United States' ... refers to the holdings, as opposed to the dicta, of this Court's decisions as of the time of the relevant state-court decision." Williams v. Taylor, 529 U.S. 362, 412, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000) (emphasis added). "In other words, `clearly established Federal law' under § 2254(d)(1) is the governing legal principle or principles set forth by the Supreme Court at the time the state court renders its decision." Lockyer v. Andrade, 538 U.S. 63, 71-72, 123 S.Ct. 1166, 155 L.Ed.2d 144 (2003). The footnote upon which Collins relies did not set forth the governing legal principle in Lane. It was merely a comment.
When the Supreme Court does not purport to interpret any provision of the Constitution, then "[t]hat alone would be enough to defeat a claim that [the] application [of the case] to state-court proceedings is `clearly established.'" Early v. Packer, 537 U.S. 3, 10, 123 S.Ct. 362, 154 L.Ed.2d 263 (2002) (per curiam). Here, Lane expressly stated that "[i]mproper joinder does not, in itself, violate the Constitution." 474 U.S. at 446 n. 8, 106 S.Ct. 725. Collins' argument that Lane applies to state courts fails for that reason as well.
In sum, we hold that neither Zafiro v. United States nor United States v. Lane establish a constitutional standard binding *1133 on the states requiring severance in cases where defendants present mutually antagonistic defenses.

IV. CONCLUSION
We conclude that the decision of the California Court of Appeal was not contrary to or an unreasonable application of clearly established federal law as determined by the Supreme Court. We therefore affirm the district court's order denying Collins' petition for a writ of habeas corpus.
AFFIRMED.
NOTES
[1]  Anderson was later convicted on the same charges at a retrial.
[2]  Courts use both the terms "mutually antagonistic" and "mutually exclusive." "Mutually exclusive defenses are said to exist when acquittal of one codefendant would necessarily call for the conviction of the other." United States v. Tootick, 952 F.2d 1078, 1081 (9th Cir.1991) (citing United States v. Adler, 879 F.2d 491 (9th Cir.1988)); see also State v. Kinkade, 140 Ariz. 91, 680 P.2d 801, 803 (Ariz.1984) ("defenses are mutually exclusive... if the jury, in order to believe the core of the evidence offered on behalf of one defendant, must disbelieve the core of the evidence offered on behalf of the co-defendant."). In contrast, in the less extreme situation where acceptance of one defense does not necessarily preclude acceptance of the other, the term "mutually antagonistic" is used. See United States v. Sherlock, 962 F.2d 1349, 1362-63 (9th Cir. 1992). However, many courts use the terms interchangeably, as does Collins. See, e.g., United States v. Throckmorton, 87 F.3d 1069, 1072 (9th Cir.1996); People v. Hardy, 2 Cal.4th 86, 5 Cal.Rptr.2d 796, 825 P.2d 781, 844 (1992). Because Zafiro, upon which Collins relies, uses the term "mutually antagonistic," so will we as well, but the distinction makes no difference for purposes of our AEDPA inquiry.
[3]  The current version of the rule provides that "[i]f the joinder of offenses or defendants in an indictment, an information, or a consolidation for trial appears to prejudice a defendant or the government, the court may order separate trials of counts, sever the defendants' trials, or provide any other relief that justice requires." Fed.R.Crim.P. 14.
