Ralph Armstrong was convicted in Arkansas state court of two counts of capital murder and sentenced to life imprisonment without the possibility of parole for killing his estranged wife and their unborn child. At trial, the court excluded under a state rule exculpatory evidence pointing to the guilt of two other women. That rule admits such evidence only where there is a direct link between the crime and the third parties implicated. Armstrong now seeks federal habeas relief under the Antiterrorism and Effective Death Penalty Act (AEDPA), arguing that this evidentiary rule is contrary to, or an unreasonable application of, clearly established federal law. The district court1 denied Armstrong’s petition, but granted him a certifícate of appealability on the issue of whether he was unconstitutionally deprived of a meaningful opportunity to present a complete defense. We now affirm.
I.
On February 14, 2004, police in Pulaski County, Arkansas found the body of Ralph Armstrong’s estranged wife, Dashunda Armstrong, burning in an abandoned van on rural McDonald Road. It was later determined that at the time she was killed, Dashunda was pregnant and that Armstrong was the child’s father. On the night of her death, Dashunda was at a hair appointment with her sister until about 1:00 am, after which she planned to meet Armstrong. Armstrong told the police that Dashunda never arrived at his house as planned. Upon investigation, the police discovered that on the night Dashunda was killed, Armstrong made several cell phone calls to a former girlfriend, Kim Waller, that were routed through a cellular tower near where Dashunda’s body was found.
When Waller spoke to police, she told them she spoke to and saw Armstrong the night of Dashunda’s death. Waller later testified that she picked up Armstrong from where the van was still burning and that Armstrong told her he set it on fire. Upon searching Armstrong’s home, police found information on a computer related to changing one’s identity. They also found letters from various creditors that revealed an ongoing and contentious divorce between Dashunda and Armstrong.
At trial, Armstrong attempted to introduce evidence to support his argument that Kim Waller and her two sisters, Karen and Yolanda, killed Dashunda. That evidence included:
[A]n audio tape which contained statements by the Waller sisters threatening to kill Dashunda Armstrong ..., the names of all three Waller sisters who had threatened his wife; records of the violent encounters between the women including a court case; records from the prosecutor’s office that showed mutual harassment between Mrs. Armstrong and Ms. Waller; and the presence of Kim Waller at the crime scene the night of the murder.
*1140Armstrong v. State, 366 Ark. 105, 233 S.W.3d 627, 636 (2006). The trial court excluded much of this evidence2 based on a rule from the Arkansas state case Zinger v. State, 313 Ark. 70, 852 S.W.2d 320 (1993), under which defendants may not introduce “ ‘evidence tending to show that someone other than the defendant committed the crime charged’ ” unless that evidence “ ‘points directly to the guilt of the third party. Evidence which does no more than create an inference or conjecture as to another’s guilt is inadmissible.’ ” Armstrong, 233 S.W.3d at 637 (quoting Zinger, 852 S.W.2d at 323). A jury subsequently convicted Armstrong of two counts of capital murder, and a judge sentenced him to life in prison without the possibility of parole.
Armstrong then filed a petition in Arkansas trial court for postconviction relief. In his petition, he argued, inter alia, that the United States Supreme Court case, Holmes v. South Carolina, 547 U.S. 319, 126 S.Ct. 1727, 164 L.Ed.2d 503 (2006), decided one day before the mandate on the direct appeal in this case was issued, rendered the trial court’s exclusion of evidence implicating the Waller sisters pursuant to Zinger unconstitutional. The trial court denied relief after a hearing, and the Arkansas Supreme Court affirmed.
Armstrong then petitioned for federal relief pursuant to 28 U.S.C. § 2254 in the Eastern District of Arkansas, presenting three federal constitutional issues. The magistrate recommended that Armstrong’s petition be dismissed, and the district court adopted the recommendation. Armstrong then filed a notice of appeal and an application for a Certificate of Appealability (COA). The district court granted the COA and certified to this Court one issue: whether the application of Zinger to exclude exculpatory evidence “unconstitutionally deprived [Armstrong] of a meaningful opportunity to present a complete defense as guaranteed by the Sixth and Fourteenth Amendments.” Armstrong v. Hobbs, No. 09-00100 BSM (E.D.Ark. Dec. 30, 2010) (order issuing certificate of appealability).
II.
A.
Under AEDPA, an application for a writ of habeas corpus may not be granted unless the state court’s 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). In Williams v. Taylor, 529 U.S. 362, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000), the Supreme Court held that “contrary to” and “unreasonable application of’ have distinct meanings. A decision is “contrary to” clearly established federal law if it “arrives at a conclusion opposite to that reached by [the Supreme Court] on a question of law,” or if it “confronts facts that are materially indistinguishable from a relevant Supreme Court precedent and arrives at a result opposite to [that of the Supreme Court].” Id. at 405, 120 S.Ct. 1495. A decision is “an unreasonable application of’ clearly established federal law if is clearly errone*1141ous, that is, if no “ ‘fairminded jurists could disagree’ on the correctness of the state court’s decision.” Harrington v. Richter, — U.S. -, 131 S.Ct. 770, 786, 178 L.Ed.2d 624 (2011) (quoting Yarborough v. Alvarado, 541 U.S. 652, 664, 124 S.Ct. 2140, 158 L.Ed.2d 938 (2004)).
The Supreme Court has noted that if the AEDPA standard is “difficult to meet, that is because it was meant to be.” Harrington, 131 S.Ct. at 786. Under AEDPA, the writ of habeas corpus is truly meant to be an extraordinary writ: “Section 2254(d) reflects the view that habeas corpus is a ‘guard against extreme malfunctions in the state criminal justice systems,’ not a substitute for ordinary error correction through appeal.” Id. (citing Jackson v. Virginia, 443 U.S. 307, 332 n. 5, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979) (Stevens, J., concurring in judgment)).
B.
In this case, Armstrong argues that Holmes v. South Carolina, 547 U.S. 319, 126 S.Ct. 1727, 164 L.Ed.2d 503 (2006) rendered the Arkansas court’s use of the evidentiary rule from Zinger v. State, 313 Ark. 70, 852 S.W.2d 320 (1993) contrary to, or an unreasonable application of, clearly established federal law.
In criminal cases, Arkansas courts exclude evidence “ ‘tending to show that someone other than the defendant committed the crime charged,’ ” unless that evidence “ ‘points directly to the guilt of the third party. Evidence which does no more than create an inference or conjecture as to another’s guilt is inadmissible.’ ” Zinger, 852 S.W.2d at 323 (quoting State v. Wilson, 322 N.C. 117, 367 S.E.2d 589, 600 (1988)). In Zinger, two criminal defendants were on trial for beating and stabbing a victim to death. The defendants attempted to introduce evidence of another murder in Louisiana, where the victim had been beaten and stabbed several times and left in a position similar to the victim in the Arkansas case. Id. These were the only links between the two murders. The Arkansas Supreme Court found that the trial court did not abuse its discretion in excluding evidence of the other murder. “ ‘Evidence of a mere motive or opportunity to commit the crime in another person, without more, will not suffice to raise a reasonable doubt about a defendant’s guilt: there must be direct or circumstantial evidence linking the third person to the actual perpetration of the crime.’ ” Id. (quoting People v. Kaurish, 52 Cal.3d 648, 276 Cal.Rptr. 788, 802 P.2d 278, 295-96 (1990)) (internal marks omitted).
In contrast, the United States Supreme Court in Holmes found unconstitutional a South Carolina rule that excluded evidence implicating third parties. The Court held that the rale impermissibly based exclusion not on the strength of the evidence at issue, but instead on the strength of the prosecution’s case as a whole. Rather than evaluating the strength of the link between the exculpatory evidence and the case at hand, the South Carolina rule excluded exculpatory evidence because “ ‘[i]n Anew of the strong evidence of appellant’s guilt — especially the forensic evidence— ... the proffered evidence ... did not raise a ‘reasonable inference’ as to the appellant’s own innocence.’ ” Id. at 328-29, 126 S.Ct. 1727 (quoting State v. Gay, 343 S.C. 543, 541 S.E.2d 541, 545 (2001)). The rale contested in Holmes thus did not rationally serve the legitimate end of focusing the trial on “central issues by excluding evidence that has only a very weak logical connection to the central issues.” Holmes, 547 U.S. at 330, 126 S.Ct. 1727. Rather, it required the trial court to evaluate the prosecution’s case itself, and if the evidence was strong enough, exclude even highly probative evidence that did not pose an undue risk of harassment, prejudice or confusion of the issues. Id.
*1142The Supreme Court in Holmes contrasted the contested South Carolina rule with another South Carolina rule, which excluded
evidence which can have no other effect than to cast a bare suspicion on another, or to raise a conjectural inference as to the commission of the crime by another.... [Bjefore such testimony can be received, there must be such proof of connection with it, such a train of facts or circumstances, as tends clearly to point out such other person as the guilty party.
Holmes, 547 U.S. at 328, 126 S.Ct. 1727 (quoting State v. Gregory, 198 S.C. 98, 16 S.E.2d 532, 534-35 (1941)). The Court noted that “[sjuch rules are widely accepted,” Holmes, 547 U.S. at 328, 126 S.Ct. 1727, and allow trial judges to exclude evidence whose probative value is outweighed by “certain other factors such as unfair prejudice, confusion of the issues, or potential to mislead the jury.” Id. at 326, 126 S.Ct. 1727. This reasoning almost certainly affirms the constitutionality of Arkansas’s Zinger rule, which is substantially similar to the widely accepted South Carolina rule. At the very least, Holmes indicates the rule in Zinger is not contrary to clearly established federal law.3
In this case, the trial court excluded evidence pointing to the Waller sisters’ guilt on the basis of the Zinger rule, concluding that “the evidence pointed to by Armstrong does no more than create a suspicion or conjecture that the Waller sisters might have played a role in Dashunda Armstrong’s death.” Armstrong, 233 S.W.3d at 637. The Arkansas court thus excluded the evidence based on the strength of the link between that evidence and the crime. This is exactly the type of analysis the Supreme Court validated in Holmes, and thus the decision in this case is not contrary to, or an unreasonable application of, clearly established federal law.
C.
Armstrong further argues that Arkansas courts have transformed the Zinger rule into a per se rule against evidence showing another committed the crime. In support of this argument, Armstrong notes that “in each case where the issue of third party guilt evidence arose, the court barred the introduction of that evidence because it allegedly did not connect the third party directly to the crime.”
Armstrong’s argument is unavailing. As we noted in Middleton v. Roper, 498 F.3d 812, 820 (8th Cir.2007), the inquiry under AEDPA is whether a state court decision is contrary to, or an unreasonable application of, clearly established federal law, not whether the state court incorrectly applied state law. Thus even if, as Armstrong asserts, the Arkansas Supreme Court misapplied the Zinger rule in his case, he is not entitled to relief unless he can also demonstrate that such misapplication is contrary to, or an unreasonable application of, clearly established federal law.
Furthermore, Armstrong’s evidence does not necessarily support his conclusion. The fact that no Arkansas appellate court has reversed on a Zinger issue does not compel the conclusion that the Zinger rule has become a blanket exclusionary rule. Many other explanations are plausible: that no criminal defendant has yet presented sufficient proof under Zinger, that courts have admitted evidence at the *1143trial level in cases where there was no appeal, or that for any other procedural or tactical reason an appeal of a trial-level Zinger decision did not reach an appellate court on the merits of the Zinger issue.
Finally, even if Armstrong is correct that Zinger has been misapplied in other cases, this fact still does not entitle him to relief. The critical inquiry under AEDPA is not whether Arkansas courts have misapplied the Zinger rule in general in criminal cases, but rather, whether their application of the rule in Armstrong’s case was contrary to, or an unreasonable application of, clearly established state law. Here, it was not.
III.
Armstrong’s other two arguments are not within the scope of the Certificate of Appealability for this case, and thus, we decline to address them. These arguments are first, whether Arkansas courts abridged Armstrong’s right to have a jury decide all the facts necessary to convict, and second, whether Arkansas courts unconstitutionally reduced the level of proof necessary for the prosecution to obtain a conviction.
AEDPA requires the issuance of a COA before a court of appeals may entertain an appeal from a habeas proceeding arising out of state court. 28 U.S.C. § 2253(c)(1)(A). A COA may issue only if the applicant “has made a substantial showing of the denial of a constitutional right.” 28 U.S.C. § 2253(c)(2). COAs are a jurisdictional requirement; if the appellate court decides a case without first obtaining a COA, it acts without jurisdiction. See Miller-El v. Cockrell, 537 U.S. 322, 336, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003).
In this case, the district court certified the following issue for appeal: “Whether the trial court’s application of the rule in Zinger v. Arkansas, 313 Ark. 70, 852 S.W.2d 320 (1993), unconstitutionally deprived petitioner of a meaningful opportunity to present a complete defense as guaranteed by the Sixth and Fourteenth Amendments?” Armstrong v. Hobbs, No. 09-00100 BSM (E.DArk. Dec. 30, 2010) (order issuing certificate of appealability). We addressed this question and answered it in the negative above. Armstrong’s other two claims are outside the scope of the issue certified for appeal and this Court does not have jurisdiction to address them.
IV.
In sum, we conclude that the Arkansas court’s decision to exclude evidence that the Waller sisters might have committed the murder of Dashunda Armstrong was not contrary to, or an unreasonable application of, clearly established federal law. The district court therefore did not err in denying habeas relief to Mr. Armstrong, and we affirm its judgment.