MEMORANDUM***
This is an appeal from the denial of a habeas petition (28 U.S.C. § 2254), filed by Carlos Varela, an Arizona state prisoner seeking to set aside, on grounds of alleged ineffective assistance of trial counsel, his conviction on two counts of child molestation and one count of sexual abuse of a child, and his resultant consecutive sentences of 15 years, 17 years, and life with eligibility for parole after 35 years. The District Court denied the petition without holding an evidentiary hearing. The District Court granted a certificate of appeal-ability with respect to two claims of ineffectiveness of counsel, but declined to grant a certificate of appealability on the lack of an evidentiary hearing.
PROCEDURAL HISTORY
Appellant Varela was tried in 1988 on charges of molesting and sexually abusing his niece. The initial alleged molestation took place when the niece was five; the sexual abuse when she was thirteen.
Prior to trial, the trial judge heard argument on two in limine prosecution motions to preclude the introduction by the defense of character testimony with respect to three of the prosecution’s witnesses — Sonya Gallardo, the alleged victim; Cynthia Gallardo, her older sister; and Gloria Gal-lardo, the mother of the two girls (appellant’s sister). The trial judge granted the motions to preclude. Trial ensued, leading to the challenged conviction and resultant sentences.
On appeal Mr. Varela was represented by new counsel. The Arizona Court of Appeals affirmed, holding that the character evidence appellant sought to admit was not probative of untruthfulness. See Ariz. R. Evid. 608(a). The court further reasoned that even if appellant was trying to prove that the victims had fabricated their stories, the character evidence — tales of the witnesses’ smoking pot, “hang[ing] out in the barrio,” and “run[ning] around”did not demonstrate a motive for the witnesses to make false accusations. Varela did not appeal to the Arizona Supreme Court.
Varela filed a pro se application for post-conviction relief in 1993, alleging ineffective assistance of trial counsel. The Arizona trial court denied the motion. Varela filed another petition in 1996, this time represented by counsel. In it, Varela argued that trial counsel had been delinquent for failing to present Varela’s claims that Gloria Gallardo had induced her *318daughters to he in retaliation for Varela’s refusal to lend her money.
The trial court denied this petition as well, and the Arizona Court of Appeals affirmed in May of 1999. The court noted that, in order “[t]o present a colorable claim for ineffective assistance of counsel,” a petitioner seeking collaterally to challenge a conviction pursuant to Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), has the burden of showing both that counsel’s performance fell below the level of competence required by Strickland, and that counsel’s deficient representation resulted in demonstrable prejudice to the petitioner at trial. After pointing out that, “where a petitioner has made an insufficient showing of prejudice, the court need not determine whether counsel’s performance was substandard,” the Arizona Court of Appeals, without undertaking an assessment of the adequacy of trial counsel’s performance, ruled that “Varela has failed to demonstrate prejudice.” The appeals court quoted from the trial judge’s minute entry denying Rule 32 relief: the trial judge had stated it as his recollection that Varela had testified at trial about the intra-family conflicts, and the trial judge had expressed the opinion that the additional testimony about the victim and her sister and mother that Varela wished to introduce could not have prevailed over the “overwhelming evidence of defendant’s guilt.”
Varela then petitioned for federal habe-as relief, and the District Court dismissed his petition without an evidentiary hearing in June of 2001. Paraphrasing the pertinent language of 28 U.S.C. § 2254(d), the District Court concluded that Varela had not shown that the Arizona Court of Appeals’ decision with respect to Strickland was “either (1) contrary to clearly established Federal law or involved an unreasonable application of that law, 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.”
Varela thereafter sought a certificate of appealability on claims that he was denied an evidentiary hearing and received ineffective assistance of counsel. The District Court concluded that Varela failed to explain what facts were in dispute that could have been resolved by an evidentiary hearing, and noted that when no factual basis for a claim has been developed in state court, an evidentiary hearing may only be held if (1) there is a new rule of constitutional law, or (2) the facts could not have been discovered earlier. 28 U.S.C. § 2254(e)(2)(A). As neither of those conditions prevailed, the District Court denied Varela’s motion for a certificate of appeala-bility with respect to his request for an evidentiary hearing.
The District Court granted the certificate of appealability on the two ineffective assistance of counsel claims: (1) counsel’s failure to make an offer of proof concerning limitation of cross-examination and preclusion of evidence; and (2) counsel’s offer of evidence under Rule 608(b) of the Arizona Rules of Evidence rather than under Rule 401, and failure to make an offer of proof to show motive and/or bias. STANDARD OF REVIEW
This court reviews a denial (or grant) of habeas corpus de novo. Bowen v. Hood, 202 F.3d 1211, 1218 (9th Cir.2000); Dow-ney v. Crabtree, 100 F.3d 662, 663-64 (9th Cir.1996); Weston v. Kernan, 50 F.3d 633, 636 (9th Cir.1995), 516 U.S. 937, 116 S.Ct. 351,133 L.Ed.2d 247 (1995).
DISCUSSION
Pretermitting the question whether Varela’s trial counsel’s representation was substandard, the Arizona Court of Appeals went directly to the issue of whether, on *319the basis of the record before it, there was reason to conclude that counsel’s allegedly substandard performance had caused Varela demonstrable prejudice. Noting that the record was “extremely limited” and that “[wjith the exception of a few excerpted pages it is devoid of any transcripts or minute entries from [Varela’s] trial and contains nothing from which we might conclude the trial court abused its discretion,” the Arizona Court of Appeals pointed out that “it is petitioner’s responsibility to see that the record contains all materials necessary to our decision,” and hence “we presume the missing material supports the actions of the trial court.” For these reasons the Arizona Court of Appeals concluded that, in view of the trial court’s “first-hand observation” of what transpired at trial “we defer to its conclusion that petitioner sustained no prejudice attributable to the alleged errors and omissions of counsel.”
With matters in this posture, the District Court concluded that the ruling of the Arizona Court of Appeals was neither inconsistent with the governing due process rules nor grounded in “an unreasonable determination of the facts” — and hence, on habeas, was unassailable. We think the reasoning and conclusions of the District Court were correct. Accordingly, the judgment of the District Court denying habeas corpus is AFFIRMED.
This disposition is not appropriate for publication and may not be cited to or by the courts of this circuit except as provided by Ninth Circuit Rule 36-3.