Defendant Gennaro Piscopo seeks review of the district court’s denial of his habeas corpus petition. Piscopo, a pastor, was sentenced by a Michigan state court to five years of probation following his conviction on one count of fourth-degree criminal sexual conduct (CSC) stemming from contact with a participant in a church ceremony. He asserts that the state trial court’s exclusion of certain evidence violated his constitutional rights to confront witnesses and present a defense. Because the adjudication of these issues by the state courts represents a reasonable application of Supreme Court precedent, we affirm.
I
Complainant KB was a participant in a deliverance ceremony at the church run by Pastor Piscopo in November 2001. Approximately 100 people were in attendance, one-third or fewer to be delivered from evil spirits, and the balance to assist with the ceremony. During the pertinent part of the events at the church that day, the deliverance participants sat on folding chairs, with church workers and/or volunteers surrounding them, yelling at or praying with the participants.
KB described her involvement in the ceremony as less than fully engaged. For this reason, she was approached by Pisco-po several times during the proceedings. KB alleged that during one of these encounters, Piscopo instructed his assistants to restrain KB while he touched and rubbed her breasts and genital area. KB described this behavior to law enforcement the day after the deliverance ceremony.
Piscopo was charged with two counts of second-degree CSC for his conduct with KB. He was also charged with separate counts of fourth-degree CSC involving two other participants in deliverance ceremonies. No physical evidence was presented at trial, and KB was the only source of evidence against Piscopo with regard to her allegations.1 At trial, Piscopo sought to introduce statements made by KB on a couple of pages of a lengthy questionnaire she submitted the day of the deliverance she attended. In that paperwork, KB stated that she had been abused by her father, also a pastor, over a 10-year period when she was a child. She also recounted her fear of demons and her belief that she had been raped by a demon as a teenager.
As described by the Michigan Court of Appeals, the trial court excluded all of the KB questionnaire evidence for the reasons that:
(1) the evidence was not relevant; (2) KB’s assertions were hearsay and did *700not fall under the business records exception argued by defendant, MRE 803(6); and (3) some of the statements were barred by the rape-shield statute, MCL 750.520j, and evidentiary rule, MRE 404(a)(3).
People v. Piscopo, No. 245835, 2004 WL 1416282, at *4, (Mich.Ct.App. June 24, 2004).
Following four and a half days of deliberation, Piscopo was convicted by a jury on one lesser-included count of fourth-degree CSC as to KB. He was found not guilty on all remaining counts, including those involving other complainants. He was sentenced to five years of probation and ordered to pay restitution.2 Piscopo’s direct appeal was unsuccessful. See id. His application for leave to appeal to the Michigan Supreme Court was ultimately denied. See People v. Piscopo, 480 Mich. 966, 741 N.W.2d 826 (2007).
Piscopo then sought habeas review of his conviction in the district court. The district court denied the petition on the merits. Piscopo appealed the district court’s decision and requested a certificate of ap-pealability from both the district court and this court, enumerating three distinct claims. The district court granted a certificate of appealability as to Piscopo’s first and second claims, which both address information given by KB in her questionnaire and allege violations of his constitutional rights.3 These are the claims before us on appeal.
II.
A. Habeas Review
We review de novo the legal conclusions made by a district court in a habeas corpus proceeding. Villagarcia v. Warden, Noble Corr. Inst., 599 F.3d 529, 533 (6th Cir.2010). Under the provisions of the Anti-terrorism and Effective Death Penalty Act of 1996, which applies to this case, a federal court may grant the writ of habeas corpus with respect to a “claim that was adjudicated on the merits in State court proceedings,” if that adjudication
(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).4
A state court decision is “contrary to” established Supreme Court law if (1) “the state court applies a rule that contradicts the governing law set forth in our cases,” or (2) “the state court confronts a set of facts that are materially indistinguishable from a decision of this Court and nevertheless arrives at a result different from our precedent.” Williams v. Taylor, 529 U.S. 362, 405-06, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000). Concerning the question of an “unreasonable application,” “a federal ha-beas court may not issue the writ simply *701because that court concludes in its independent judgment that the relevant state-court decision applied clearly established federal law erroneously or incorrectly. Rather, that application must also be unreasonable.” Id. at 411, 120 S.Ct. 1495.
B. Sexual Abuse by Pastor-Father
We will first address the statements in KB’s questionnaire concerning the alleged abuse by her father, also a pastor.5 In that document, KB wrote that when she was seven years old, her father “stood naked in the bathtub, soaped up, tried to get [her] to touch him,” and that this continued for 10 years. When cross-examining her on this statement for purposes of making an appellate record, outside of the hearing of the jury, defense counsel asked KB if it would surprise her if her father told an investigator KB’s allegations were untrue.
In his brief, Piscopo states that this evidence was admissible to show that KB’s perception of the events at the deliverance ceremony was unreliable. He states that his “argument to the jury would have been that [KB] had a bias against male pastors because of her bad experiences with a pastor who happened to also be her father,” and that this bias “caused her to perceive the touchings as sexual when in fact they were not.”
At the time of the deliverance ceremony, KB (according to her handwritten document) was 43 years old. The accuracy of the reported abuse by her father, decades in the past, was questioned by defense counsel in the record he made for appeal. This suggests that defense counsel wanted to admit the evidence of KB’s allegations, as well as shed uncertainty upon their accuracy. We question how evidence of sexual abuse by KB’s father (whether the jury learned that such abuse was disputed by the father or not) could be used to show a propensity on the part of KB to consider much later, physical contact by a pastor to be sexual in nature. Piscopo does not develop any theory as to why the fact that KB’s father was a pastor might cause her to single out other pastors for false accusations of offensive sexual conduct.
Under the Sixth Amendment, a criminal defendant is guaranteed the right to confront “witnesses against him.” U.S. Const. amend. VI. In Davis v. Alaska, 415 U.S. 308, 94 S.Ct. 1105, 39 L.Ed.2d 347 (1974), the Supreme Court found that the state trial court had violated the defendant’s Sixth Amendment rights by failing to allow his impeachment of a prosecution witness — a juvenile — with that witness’s prior criminal record. Id. at 310-11, 94 S.Ct. 1105. In the case of Delaware v. Van Arsdall, 475 U.S. 673, 106 S.Ct. 1431, 89 L.Ed.2d 674 (1986), which examined the Davis case, the Supreme Court emphasized that the trial court has “wide latitude” to impose “reasonable limits” to avoid “harassment, prejudice, confusion of the issues, the witness’ safety, or interrogation that is repetitive or only marginally relevant.” Id. at 679, 106 S.Ct. 1431. In *702Van Arsdall, the defendant sought to impeach a witness whose drunkenness charge was dropped after he agreed to talk to the prosecutor about the defendant’s case. That court found a Sixth Amendment violation where the trial court had “prohibited all inquiry into the possibility that [the witness] would be biased as a result of the State’s dismissal of his pending public drunkenness charge.” Id.
In our decision in Boggs v. Collins, 226 F.3d 728 (6th Cir.2000), the habeas action of a defendant convicted of rape, we considered the trial court’s exclusion of evidence of a prior, allegedly false accusation of rape. Determining that the desired cross-examination was an intended attack on the witness’s general credibility, and finding no plausible defense theory of motive or bias, we found no constitutional violation in its exclusion. Id. at 740. We considered the Davis and Van Arsdall cases in concluding “that cross-examination as to bias, motive or prejudice is constitutionally protected, but cross-examination as to general credibility is not.” Boggs, 226 F.3d at 737. As the parties recognize, this “rule” noted in Boggs was vigorously questioned by our decision in Vasquez v. Jones, 496 F.3d 564, 574 (6th Cir.2007). In Vasquez, we held that the trial court’s refusal to allow a defendant to impeach hearsay testimony with a witness’s prior criminal record violated the Confrontation Clause. We held the proposition to be equally true whether the cross-examination went to credibility or bias. We found the Boggs case nondispositive on several fronts, including the trial court’s reliance on the rape shield statute, and distinguishable facts.6
Regardless of whether Piscopo sought to admit this evidence as an attack on KB’s credibility, generally, or more specifically to show a bias or motive on the part of KB, the state appellate court did not unreasonably apply Supreme Court precedent in upholding its exclusion. The instant case does not involve a “prototypical form of bias,” as did the Van Arsdall and Davis cases. The assertion that the questionnaire answers reveal a bias against pastors is speculative. Nonetheless, defense counsel was allowed to pursue this argument. On more than one occasion defense counsel did tell the jury that KB had been abused by men, in particular her father, and also told the jury that KB had filled out “paperwork” indicating that she had issues with men and her father. At closing, defense counsel argued that
[y]ou cannot put a burden on us to find out why KR and KB testified the way they did. Did they have pre-set ideas in their head of what was happening? Did they have some fears? I don’t know who’s been involved in a car accident, but if you’re behind that wheel, and you’re-you’re like this. You’re jumpy. That’s normal, human reaction. We don’t know if these, what their backgrounds were, whether they were jumpy around men, whether they had trouble with Pastor, whether they had trouble with men. We weren’t allowed to find *703out. But if they were, and someone came up after they’re in an altered state of consciousness, as Jim Bacon testifies, and scares them, they’re going to imagine all kinds of things happened.
As noted by the district court, the questioning of KB on this evidence by defense counsel suggests that, at that juncture, the defense intended to use the evidence to show a prior false accusation of sexual abuse. Such evidence would be used to attack KB’s credibility, not to show a bias. In any event, as both the Michigan Court of Appeals and the district court noted, the allegations against KB’s father are “removed in time and markedly different” from those made against Piscopo.
Given the multiple possible reasons counsel sought to have the evidence admitted, the trial court’s ruling was not inconsistent with Davis or Van Arsdall. The Michigan court’s conclusion that Piscopo’s rights under the Confrontation Clause were not violated by the exclusion of this evidence was not unreasonable.
C. Demon Statements
Piscopo also asserts his constitutional right to confront witnesses and present a defense was violated by the trial court when it did not admit KB’s statements concerning her asserted rape and threats by demons.7 Piscopo contends that such evidence would have shown the jury that KB misperceived what happened to her during the deliverance ceremony, and that her “delusions” rendered her testimony unreliable.
As noted above, the defendant was permitted to make a record of testimony concerning this evidence outside of the presence of the jury. KB confirmed that she wrote on her deliverance questionnaire that she was raped by a demon as a teenager. She explained that she was lying in bed and sensed the presence of a “spirit” without a human form. She also acknowledged writing that evil spirits had tried to kill her and her sister, and she had told people of her fear of the basement stairs because she was afraid that demons would grab her by the ankles.
Piscopo’s argument concerning KB’s experience with demons was mentioned only in passing by the opinion of the Michigan Court of Appeals. On habeas review, the district court then determined that because the state court of appeals decision “provided only a cursory analysis of demon-rape issue,” the appropriate standard of review to apply was that of “modified AEDPA deference.” “This standard of review requires the court to conduct a careful review of the record and applicable law, but nonetheless bars the court from reversing unless the state court’s decision is contrary to or an unreasonable application of federal law.” Maldonado v. Wilson, 416 F.3d 470, 476 (6th Cir.2005).
As the state asserts, however, all of the deference afforded by § 2264 applies to our review. This is true whether or not “a state court’s order is unaccompanied by an opinion explaining the reasons relief has been denied.” Harrington v. Richter, 562 U.S. —, 131 S.Ct. 770, 784, 178 L.Ed.2d 624 (2011). See also Treesh v. Bagley, 612 *704F.3d 424, 429 (6th Cir.2010), cert. denied, — U.S. —, 131 S.Ct. 1678, 179 L.Ed.2d 622 (2011). The Supreme Court’s recent Harrington opinion described the AEDPA’s role as a “part of the basic structure of federal habeas jurisdiction, designed to confirm that state courts are the principal forum for asserting constitutional challenges to state convictions.” Harrington, 131 S.Ct. at 787, 131 S.Ct. 770. A state court order lacking in reasoning or explanation does not have to include citation to, or demonstrate its awareness of, Supreme Court decisions as long as any reasoning that is given, and the result, are not in conflict with Supreme Court precedent. Treesh, 612 F.3d at 430 (citing Williams v. Bagley, 380 F.3d 932, 942 (6th Cir.2004)).
As with the sexual abuse evidence, the parties also dispute the characterization of this evidence. Piscopo asserts that the evidence would have been used to show that KB misperceived the incident, rather than to attack her credibility. This is asserted by Piscopo to distinguish the case from the facts of Boggs, where we found that “cross-examination as to general credibility is not [constitutionally protected].” 226 F.3d at 737. However, as discussed above, in Vasquez, we held that attacks on general credibility were protected under the Confrontation Clause.8
There is no need to address the tension between the Boggs and Vasquez decisions in deciding this case. Even if Piscopo’s intended use of the evidence was as described, it was not unreasonable for the Michigan courts to conclude that it was a constitutionally permitted limit on cross examination. The jury was presented with the circumstances of the contact between KB and Piscopo. Members of the jury were aware that KB was someone who claimed to be plagued by evil spirits and was in fact at the deliverance ceremony to exorcise them. The jury also heard testimony concerning her attendance at other pastors’ deliverance ceremonies in the past. KB filled out a lengthy form, including a couple of pages briefly describing upsetting experiences in her life, in preparation for deliverance by Piscopo from evil spirits. Piscopo does not argue that these past incidents somehow incapacitated KB, or caused her to be generally unable to distinguish real life events from imagined ones. He offers no argument as to how one questionnaire answer concerning KB’s perceived teenage demon rape demonstrates that she incorrectly sexualizes situations as an adult.9
The Supreme Court has described the Confrontation Clause’s guarantee as that *705of “an opportunity for effective cross-examination, not cross-examination that is effective in whatever way, and to whatever extent, the defense might wish.” Delaware v. Fensterer, 474 U.S. 15, 20, 106 S.Ct. 292, 88 L.Ed.2d 15 (1985). Whether or not we would have come to the same conclusion as the trial court on these evi-dentiary questions is not dispositive of this action. See Bell v. Cone, 535 U.S. 685, 699, 122 S.Ct. 1843, 152 L.Ed.2d 914 (2002).
As the Supreme Court stated in Harrington, habeas corpus is not a “substitute for ordinary error correction through appeal.” Harrington, 131 S.Ct. at 786. Ha-beas review employs a deference which “demands that state-court decisions be given the benefit of the doubt.” Montgomery v. Bobby, 654 F.3d 668, 676 (6th Cir.2011) (quoting Cullen v. Pinholster, — U.S. —, 131 S.Ct. 1388, 1398, 179 L.Ed.2d 557 (2011)). Application of that deference to the state court rulings at issue here demonstrates that Piscopo is not entitled to the relief that he seeks.
Because the decision in the Michigan state courts — that excluding this evidence represented a constitutionally permitted limit on Piscopo’s cross-examination of KB — was not an unreasonable application of Supreme Court precedent, we AFFIRM the district court’s denial of the petition.