Before HIGGINBOTHAM, JONES, and COSTA, Circuit Judges. PATRICK E. HIGGINBOTHAM, Circuit Judge:John Hummel seeks a certificate of appealability to appeal the district court’s denial of his federal habeas corpus petition under 28 U.S.C. § 2254. We find that Hummel has not shown that jurists of reason could debate whether the district court erred in denying his petition, and so we must deny his application.IKennedale, Texas authorities responded to a fire at Hummel’s house shortly after midnight on December 18, 2009. Hummel’s pregnant wife, father- in-law, and five-year-old daughter were found dead inside. Hummel was not inside the house, and approached an officer outside around 4:30 a.m. He told police that he was away from the house the entire night because he was checking prices for Christmas presents. During the interview, police observed what appeared to be blood on his pants; they took his clothing for testing and observed more blood on one of his socks and scratch marks on his back. After leaving the police department, Hummel picked up a paycheck from his employer and subsequently went missing.Two days later, Hummel attempted to enter the United States on foot at a port of entry between Tijuana, Mexico, and San Ysidro, California, without a passport or other acceptable proof of citizenship. Upon entering his name and date of birth into the computer system, the Customs and Border Protection officer was alerted that Hummel was a missing person and might be armed and dangerous. The alert stated that if Hummel was located, CBP should contact the Kennedale Police Department, but should not arrest or detain him. The officer called the Kennedale Police Department, which said to hold Hummel based on an arson arrest warrant, though no warrant had been approved at that point. CBP learned shortly after that there was no active warrant, but continued to detain Hummel until a warrant was issued later that day. After the warrant was issued, Kennedale police officers traveled to the San Diego jail where Hummel was being held, read him his Miranda rights, and interrogated him. Hummel confessed orally and in writing to killing all three victims, setting the house on fire, dumping the weapons he had used, and driving to several Walmart stores “to be seen on camera.” Based on this information, authorities found several weapons in a dumpster that tested positive for DNA from Hummel and his family members. Hummel’s clothing from that night tested positive for DNA from Hummel’s wife.The prosecution presented this evidence at trial, in addition to testimony from Kristie Freeze, who had a relationship with Hummel while divorcing her husband. She said that she had told Hummel not to contact her after she learned his wife was pregnant, about a week before the murders, but he continued to call and text her. She also testified that she told Hummel on December 16 that her divorce became final—two days before the murders.The jury convicted Hummel of capital murder. At the punishment stage of the trial, the jury was asked to determine whether there was a probability that Hummel “would commit criminal acts of violence that would constitute a continuing threat to society” and whether “[t]aking into consideration all of the evidence, including the circumstances of the offense, [Hummel's] character and background, and [Hummel's] personal moral culpability,” it found sufficient mitigating circumstances to warrant life imprisonment rather than death. It found that Hummel was likely to be a future danger and that there were no such mitigating circumstances. The Texas Court of Criminal Appeals affirmed the judgment and sentence on direct appeal. Hummel’s state habeas application was subsequently denied by the trial court and the Court of Criminal Appeals.[1] The district court denied Hummel’s federal habeas petition and denied his application for a COA.IIA state prisoner does not have “an absolute right to appeal” from a federal district court decision denying a petition for a writ of habeas corpus.[2] Instead, the prisoner must obtain a certificate of appealability.[3] This requires a “substantial showing of the denial of a constitutional right”[4]—that “jurists of reason could disagree with the district court’s resolution of [the applicant's] constitutional claims or that jurists could conclude the issues presented are adequate to deserve encouragement to proceed further.”[5] We undertake a threshold inquiry, not a full-fledged merits analysis, to determine whether the applicant’s claims are reasonably debatable.[6]Hummel’s petition is “also subject to the deferential standards of AEDPA.”[7] For Hummel to be entitled to federal habeas relief under 28 U.S.C. § 2254(d), he must show that the state court’s decision was “contrary to” or “involved an unreasonable application of” clearly established federal law, or that it “was based on an unreasonable determination of the facts” given the record before the state court.[8] It is not enough for the state court to have been incorrect in its application of law or determination of facts; it must also have been unreasonable.[9]In sum, we must determine whether jurists of reason could debate the district court’s conclusion that the state court decision in Hummel’s case was not contrary to clearly established federal law, did not unreasonably apply that law, and did not unreasonably determine the facts. Finding that no reasonable jurist could debate this, we deny Hummel’s application for a COA.IIIFirst, Hummel argues that he received ineffective assistance of trial counsel in violation of the Sixth Amendment. Under Strickland v. Washington, to show constitutionally deficient assistance of counsel, Hummel must establish “(1) that counsel’s representation fell below an objective standard of reasonableness and (2) that the deficient representation caused prejudice, which requires a showing that there is a reasonable probability that, but for counsel’s unprofessional errors, the result of the proceeding would have been different.”[10] Our scrutiny of counsel’s performance is “highly deferential,”[11] and “doubly” so when the ineffective-assistance claim is raised on federal review of a state court decision that rejected the Strickland claim on the merits.[12]Reasonable jurists cannot debate the reasonableness of the district court’s conclusion that Hummel failed to clear this high bar. Hummel argues that the defense should have presented testimony from jail deputies who interacted with Hummel prior to trial, to testify that he was not a high-risk inmate and was unlikely to be a future danger. He also argues that trial counsel should have presented expert mental health testimony that he was unlikely to be a future danger, in part based on an assessment that the crime was triggered by complex post-traumatic stress disorder due to attachment trauma. But trial counsel presented extensive evidence from expert and lay witnesses that Hummel was unlikely to be a future threat, including evidence of his good behavior while in jail and his nonviolent and non-criminal history.[13] Counsel made a reasonable strategic decision not to seek testimony from jail personnel, as Hummel had indicated he had no especially positive relationships with anyone at the jail,[14] and a similarly reasonable decision not to present specific expert testimony based on methods that could have opened the door to powerful rebuttal testimony from the state’s expert.[15] As the State observes, Hummel’s argument boils down to a matter of degree. He argues not that the defense should have adopted an entirely different theory, but that it failed to present available, helpful evidence on the theory it had adopted—a difficult route by which to demonstrate ineffective assistance.[16]Several of Hummel’s other ineffective-assistance arguments fail for the same reason. He argues that counsel should have presented expert testimony on Hummel’s social history beyond the neuropsychological evaluation Dr. McGarrahan provided; that it should have called additional lay witnesses to testify to his childhood trauma and nonviolent nature; and that it should have presented further evidence of his military service. We cannot debate the district court’s deference to the state court’s conclusions that counsel presented considerable evidence of Hummel’s life circumstances—and that counsel was not constitutionally deficient in failing to package this evidence in exactly the way Hummel may now prefer. We also cannot debate its deference to the conclusion that counsel made acceptable strategic choices not to present testimony that could have been double-edged, such as further evidence about Hummel’s military service.[17]Hummel finally argues that trial counsel should have contested the sufficiency of the State’s evidence of future dangerousness. The prosecution’s future-dangerousness case centered on the murders themselves, evidence that Hummel had attempted to poison his family two days before the murders by placing rat poison in their food, and evidence of Hummel’s sexually deviant activity and illegal drug use. Trial counsel argued to the jury that the State had not proved future dangerousness, repeatedly noting the lack of evidence that Hummel had ever been violent previously. Hummel offers no reason to doubt the state court’s determination that the State’s evidence was sufficient to support a finding of future dangerousness, so he has not shown that reasonable jurists could debate the district court’s conclusion that counsel was not deficient in failing to further object to the sufficiency of the evidence.[18]On the record before the state court—and especially with the “double” deference we afford to a Strickland claim on habeas review—reasonable jurists could not debate the district court’s decision not to grant habeas relief on Hummel’s claim for ineffective assistance of trial counsel.IVSecond, Hummel argues that he received ineffective assistance of appellate counsel. We review an ineffective-assistance-of-appellate-counsel claim on habeas review in much the same way that we review claims for ineffective assistance of trial counsel, but we are mindful that “winnowing out weaker arguments on appeal and focusing on those more likely to prevail, far from being evidence of incompetence, is the hallmark of effective appellate advocacy.”[19]At trial, Hummel unsuccessfully moved to suppress the statements he made to police after being apprehended, claiming in part that Customs and Border Protection had unlawfully detained him before an arrest warrant was issued. His appellate counsel appealed the denial of the motion to suppress, but focused on the Kennedale Police Department’s false representation to CBP that they had already secured an arrest warrant, arguing that without that false representation CBP would not have detained Hummel. Hummel avers that his appellate counsel was unconstitutionally deficient in failing to argue specifically that CBP lost jurisdiction to detain Hummel once they learned that no warrant had been issued.The state habeas court concluded that Hummel failed to demonstrate that he would have prevailed on appeal if his appellate counsel had raised more clearly the “jurisdiction-dropping” argument—both because Hummel’s “detention by CBP pending the issuance of an arrest warrant was justified on several grounds based on federal law and CBP’s policies,” and because even if appellate counsel had successfully argued that Hummel’s detention was illegal, Hummel’s confession was sufficiently attenuated from the detention that it should not have been suppressed regardless. Hummel does not point to federal law clearly prohibiting CBP from detaining him upon learning that there was no active warrant for Hummel’s arrest, given that he had attempted to enter the United States without a passport.[20] He similarly does not present clearly established law undercutting the state court’s conclusion that his confession was sufficiently attenuated from any illegality in the detention.[21]The federal courts’ task is not to establish whether CBP had authority to detain Hummel, whether the state court reasonably concluded that CBP had authority to detain Hummel, or whether Hummel’s appellate counsel was unconstitutionally deficient in failing to straightforwardly raise this specific argument on direct appeal. We must instead determine whether the district court erred in determining that the state court did not unreasonably conclude that Hummel’s appellate counsel’s strategy fell within the “wide range of reasonable professional assistance” and that any failures by appellate counsel did not prejudice Hummel.[22] None could debate its holding that the state court was not unreasonable in drawing these conclusions.VThird, Hummel argues that Texas Code of Criminal Procedure Article 37.071, the basis for the jury instructions on the special questions at the punishment phase, unconstitutionally limits the jury’s ability to consider mitigating evidence that goes beyond a defendant’s “moral blameworthiness.”[23] We have consistently concluded, in the face of similar arguments, that “[t]he statute does not unconstitutionally restrict the mitigating evidence that Texas juries are allowed to consider.”[24] We have held that Article 37.071 § 2(e)(1) offers a “broad definition of mitigating evidence” that is not limited by § 2(f)(4)’s reference to “moral blameworthiness.”[25]Hummel’s argument cannot support a holding that the state court unreasonably applied clearly established federal law.[26]VIWe deny Hummel’s application for a certificate of appealability.