7
    Id.
 2
8

    Id.
 2
9

    Id. at 998.
                                6
silent.30 The District Court denied the petition, explaining that
Rosen failed to show that the Pennsylvania Supreme Court’s
conclusion that there was no Fifth Amendment violation ran
afoul of clearly established federal law.31 The court explained
that Rosen “relies on snippets from several Supreme Court
cases and a Third Circuit case, in an attempt to extrapolate
‘clearly established Federal law’ from general principles and
materially distinguishable holdings of the Supreme Court.”32
Thus, the District Court concluded that Rosen had failed to
overcome the deference owed to state court decisions under the
Antiterrorism and Effective Death Penalty Act of 1996
(AEDPA).33

II.      JURISDICTION AND STANDARD OF REVIEW
      A. Jurisdiction

       Rosen brought this habeas corpus action under 28
U.S.C. § 2254. The District Court had jurisdiction under 28
U.S.C. §§ 2241(a) and 2254(a). The order of the District Court
dismissing the petition is an appealable final order. The District
Court denied a certificate of appealability, but we later granted
one on Rosen’s claimed Fifth Amendment violation.34
Jurisdiction for this appeal arises under 28 U.S.C. § 1291 and
28 U.S.C. § 2253(c)(1).

      B. Standard of Review under AEDPA

       We exercise plenary review over the District Court’s
denial of Rosen’s habeas petition.35 The Pennsylvania
Supreme Court decided the Fifth Amendment issue on the
merits. Therefore, pursuant to 28 U.S.C. § 2254(d), AEDPA
requires Rosen to show that the state court ruling:
       (1) resulted in a decision that was contrary to, or
       involved an unreasonable application of, clearly


 30
    Rosen v. Kerestes, Civil Action No. 15-4539, 
2018 WL
 4030740 
(E.D. Pa. Aug. 22, 2018).
 31

    Id. at *1 
n.1.
 32

    Id.
 33
    Id.
 34
    A3.
 35
    Ross v. Dist. Atty. Allegheny Cnty., 
672 F.3d 198
, 205
 (3d Cir. 2012).
                                7
       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.36

      In Williams v. Taylor, 
529 U.S. 362 
(2000), the
Supreme Court elaborated on § 2254(d)(1), explaining:
       Under the “contrary to” clause, a federal habeas
       court may grant the writ if the state court arrives
       at a conclusion opposite to that reached by this
       Court on a question of law or if the state court
       decides a case differently than this Court has on
       a set of materially indistinguishable facts. Under
       the “unreasonable application” clause, a federal
       habeas court may grant the writ if the state court
       identifies the correct governing legal principle
       from this Court's decisions but unreasonably
       applies that principle to the facts of the prisoner's
       case.37

       We have further explained that a state court decision is
“contrary to” clearly established law where “the Supreme
Court has established a rule that determines the outcome of the
petition.”38 “[I]t is not sufficient for the petitioner to show
merely that his interpretation of Supreme Court precedent is
more plausible than the state court’s; rather, the petitioner must
demonstrate that Supreme Court precedent requires the
contrary outcome.”39

       A state court’s decision is an “unreasonable
application” of clearly established law where “evaluated
objectively and on the merits, [it] resulted in an outcome that
cannot reasonably be justified under existing Supreme Court
precedent. In making this determination, mere disagreement
with the state court's conclusions is not enough to warrant

 36
    28 U.S.C. § 2254(d).
 
37
    Will. v
. Taylor, 
529 U.S. 362
, 412-13 (2000).
 38
    Matteo v. Superintendent, SCI Albion, 
171 F.3d 877
, 888
 (3d Cir. 1999) (en banc), cert. denied 
528 U.S. 824 
(1999).
 39

    Id. (emphasis in the 
original).
                                8
habeas relief.”40 Importantly, this entails a “substantially
higher threshold” than a federal court’s independent judgment
that the state court’s application of Supreme Court precedent
was incorrect.41 Instead, the state court’s application of federal
law must be objectively unreasonable, not merely incorrect.42

       Section 2254(d)(2), in turn, sharply restricts the
circumstances in which a federal habeas court may grant relief
based on a state court’s factual determinations. The petitioner
must show that the state court verdict was based on an
unreasonable determination of the evidence and that a
reasonable factfinder could not have reached the same
conclusion.43
III. DISCUSSION
    A. Rosen failed to demonstrate that using his
       statements to the Commonwealth’s psychiatric
       expert to impeach him at his second trial would be
       contrary to or an unreasonable application of clearly
       established Fifth Amendment law.
        We have previously described our approach to §
2254(d)(1) as a two-step analysis whereby “federal habeas
courts first . . . identify whether the Supreme Court has
articulated a rule specific enough to trigger ‘contrary to’
review; and second, only if it has not, . . . evaluate whether the
state court unreasonably applied the relevant body of
precedent.”44 The plain language of § 2254(d)(1) applies to “a
decision that was contrary to, or involved an unreasonable
application of, clearly established Federal law”—applying the
latter to both the “contrary to” and “unreasonable application”
prongs of § 2254(d)(1).45 As we acknowledged in Matteo, there


 40

    Id. at 890.
 41
    Renico v. Lett, 
559 U.S. 766
, 773 (2010) (citing Schriro
 v. Landrigan, 
550 U.S. 465
, 473 (2007)).
 42
     
Williams, 529 U.S. at 410
 (“[A]n unreasonable application of federal law is different
 from an incorrect application of federal law.”) (emphasis
 in the original).
 43
    Campbell v. Vaughn, 
209 F.3d 280
, 291 (3d Cir. 2000).
 44
    
Matteo, 171 F.3d at 888
.
 45
    See 
Williams, 529 U.S. at 412 
(“Under § 2254(d)(1), the
 writ may issue only if one of the following two conditions
                                9
is likely some overlap amongst the parts of § 2254(d)(1), “but
we must attempt to read the statute so that each has some
operative effect . . . .”46

       Accordingly, identifying an applicable principle of
clearly established Supreme Court law can be treated as a
prerequisite—or Step 0.5—to applying the two-step test from
Matteo. This approach is consistent with our decision in
Fischetti v. Johnson, where we explained that § 2254(d)(1)
“requires us to determine what the clearly established Supreme
Court decisional law was at the time petitioner’s conviction
became final[,]” and then “analyze the challenged state
decision in light of that decisional law under each of the two
prongs of the AEDPA test.”47

       “Clearly established” Supreme Court law “refers to the
holdings, as opposed to the dicta, of [the Supreme] Court’s
decisions as of the time of the relevant state-court decision.”48
Furthermore, in determining what is “clearly established,”
Supreme Court decisions cannot be viewed “at a broad level of
generality,” but instead must be viewed on a “case-specific
level.”49 The “clearly established Federal law” provision
requires Supreme Court decisions to be viewed through a
“sharply focused lens.”50

 is satisfied—the state-court adjudication resulted in a
 decision that (1) ‘was contrary to . . . clearly established
 Federal law, as determined by the Supreme Court of the
 United States,’ or (2) ‘involved an unreasonable
 application of . . . clearly established Federal law, as
 determined by the Supreme Court of the United States.’”).
 While Matteo was decided before Williams, we have since
 affirmed that the analytical framework from Matteo
 remains applicable. See Werts v. Vaughn, 
228 F.3d 178
,
 197 (3d Cir. 2000).
 46
    
Matteo, 171 F.3d at 888
; see also Lindh v. Murphy, 
521
 U.S. 320
, 336 (1997) (“[I]n a world of silk purses and pigs’
 ears, [AEDPA] is not a silk purse of the art of statutory
 drafting.”).
 47
    Fischetti v. Johnson, 
384 F.3d 140
, 148 (3d Cir. 2004).
 48
    
Williams, 529 U.S. at 412
.
 49
    
Fischetti, 384 F.3d at 148
.
 50

    Id. at 149
.
                               10
        1. Clearly Established Supreme Court Law on the Fifth
      Amendment
       Rosen claims that it is clearly established federal law
that impeaching a defendant using evidence from the
government’s mental health expert after a mental health
defense is abandoned violates the Fifth Amendment. Rosen
draws this proposed principle primarily from three Supreme
Court cases: Estelle v. Smith, 
451 U.S. 454 
(1981); Buchanan
v. Kentucky, 
483 U.S. 402 
(1987); and Kansas v. Cheever, 
571
U.S. 87 
(2013). Rosen further relies on our decision in Gibbs
v. Frank, 
387 F.3d 268 
(3d Cir. 2004), although he concedes
that Gibbs is not clearly established Supreme Court law.51
        Rosen primarily relies upon Estelle v. Smith. There, the
Supreme Court held that a “criminal defendant, who neither
initiates a psychiatric evaluation nor attempts to introduce any
psychiatric evidence, may not be compelled to respond to a
psychiatrist if his statements can be used against him at a
capital sentencing proceeding.”52 The trial judge had sua
sponte ordered an evaluation to determine the defendant’s
competency to stand trial.53 The prosecution later used
statements from that exam in a capital sentencing proceeding
as evidence of the defendant’s future dangerousness.54 The
defendant was sentenced to death.55 On appeal, the Supreme
Court reversed the sentence. It held that the Fifth Amendment
precluded the use of the defendant’s compelled statements

 51
    The state court judgment must not merely be contrary to
 law as articulated by any federal court; rather “[i]t must
 contradict ‘clearly established’ decisions of the United
 States Supreme Court alone.” 
Fischetti, 384 F.3d at 147
.
 However, “[i]n determining whether a state decision is an
 unreasonable application of Supreme Court precedent, this
 court has taken the view that decisions of federal courts
 below the level of the . . . Supreme Court may be helpful . .
 . in ascertaining the reasonableness of state courts’
 application of clearly established . . . Supreme Court
 precedent.”
 Id. at 149 
(internal quotation marks and
 citation omitted).
 52
    
Estelle, 451 U.S. at 468
.
 53

    Id. at 456-57.
 54
    Id. at 459-60.
 55

    Id. at 460.
                              11
against him at the penalty phase where he introduced no
psychiatric evidence in his defense.56 The Court emphasized
the compelled nature of the defendant’s statements, which
were given in custody, pursuant to a court order, without
counsel present, and in the absence of Miranda warnings.57
Because the defendant was compelled to submit to the
evaluation and had not attempted to introduce any psychiatric
evidence of his own, the statements were inadmissible unless
the psychiatrist apprised the defendant of his rights and
obtained a valid waiver before questioning him.58

        Rosen also relies on Buchanan v. Kentucky, 
483 U.S.
402 
(1987). In Buchanan, the defendant raised an extreme
emotional disturbance defense at his murder trial and called his
former social worker to testify in his defense.59 The prosecutor
cross-examined the social worker using the report from a court-
ordered exam that defense counsel and the prosecutor had
jointly requested for the purpose of seeking mental health
treatment for the defendant.60 The Supreme Court found no
Fifth Amendment violation, explaining that “if a defendant
requests such an evaluation or presents psychiatric evidence,
then, at the very least, the prosecution may rebut this
presentation with evidence from the reports of the examination
that the defendant requested.”61 The Court distinguished
Estelle because defense counsel here had jointly requested the
exam and the defendant had placed his own mental health at
issue.62 The Court concluded that “[t]he introduction of such a
report for this limited rebuttal purpose does not constitute a
Fifth Amendment violation.”63



 56

    Id. at 468.
 57
    Id. at 468-69.
 58

    Id. As we have 
noted, we will assume arguendo that
 Rosen likewise was not apprised of his rights and did not
 waive his right to remain silent before his psychiatric
 exam.
 59
    
Buchanan, 483 U.S. at 408-09
.
 60

    Id. at 409-11.
 61
    Id. at 422-23.
 62

    Id. at 423.
 63

    Id. at 423-24.
                              12
        The Supreme Court in Kansas v. Cheever, 
571 U.S. 87
(2013), applying Buchanan, found that the Fifth Amendment
allowed the prosecution to introduce statements from a
compelled mental health evaluation to rebut a mental health
defense.64 At his murder trial, the defendant in Cheever offered
a psychiatric expert to support his defense that voluntary
intoxication had rendered him incapable of premeditation.65
The state offered rebuttal testimony from the defendant’s
court-ordered psychiatric examination.66 The Supreme Court
held: “where a defense expert who has examined the defendant
testifies that the defendant lacked the requisite mental state to
commit a crime, the prosecution may offer evidence from a
court-ordered psychological examination for the limited
purpose of rebutting the defendant’s evidence.”67 The Court
explained that once a defendant presents expert psychological
evidence, the government cannot be denied “the only effective
means of challenging that evidence: testimony from an expert
who has also examined him.”68 The Court emphasized that the
compelled testimony was used “only after” the defendant
placed his mental health at issue and for the purpose of
rebutting the mental health defense.69

       Although our decision in Gibbs is not Supreme Court
law, it is the most factually analogous case to Rosen’s and
assists our inquiry into what is “clearly established” Fifth
Amendment law in this court.70 There, Gibbs raised a mental


 64
    
Cheever, 571 U.S. at 93-95
.
 65

    Id. at 91.
 66
    Id. at 91-92.
 67
    Id. at 98.
 68

    Id. at 94
.
 69

    Id. at 95.
 70
    
Fischetti, 384 F.3d at 149 
(“In determining whether a
 state decision is an unreasonable application of Supreme
 Court precedent . . . decisions of federal courts below the
 level of the . . . Supreme Court may be helpful . . . in
 ascertaining the reasonableness of state courts’ application
 of clearly established . . . Supreme Court precedent.”)
 (internal quotation marks and citation omitted). And while
 the Pennsylvania Supreme Court is not bound by Gibbs, it
 is a binding precedent in the District Court with respect to
                               13
infirmity defense at his first murder trial.71 The
Commonwealth’s expert, Dr. Sadoff, testified at the first trial
to rebut Gibbs’ expert testimony on diminished capacity.72
That testimony introduced several inculpatory statements
Gibbs made during the court-ordered exam.73 After his
conviction was overturned on other grounds, Gibbs decided not
to raise a mental health defense at his second trial. Instead, he
contested the identity of the shooter.74 Nevertheless, the trial
court allowed Sadoff to testify during the Commonwealth’s
case-in-chief.75 That testimony included Gibbs’ inculpatory
statements to Sadoff during his psychiatric interview.76 On
habeas review, we found that the trial court’s decision, as
affirmed by the Pennsylvania Superior Court, was an
unreasonable application of clearly established Supreme Court
law and granted Gibbs’ habeas petition.77 Importantly, we
granted the petition based on the limited scope of the Miranda
warnings given to Gibbs, which misstated the consequences of
his Fifth Amendment waiver—an issue not relevant to Rosen’s
appeal.78 However, we also stated that if Gibbs had not been
Mirandized at all—as Rosen claims he was not—“the state
ruling admitting the Gibbs interview in the second trial [would
be] contrary to [Estelle v.] Smith itself.”79 In justifying this
conclusion, we explained that “Sadoff was permitted to testify
in the prosecution case in chief… simply to repeat
incriminating statements that Gibbs had made.”80 This was
problematic because those statements were offered “simply for
the truth of the admissions of fact” and “not even to prove a
psychological point, since the second trial presented no
psychological issue before Sadoff testified.”81

 what constitutes an unreasonable application of Fifth
 Amendment law on habeas review.
 71
    
Gibbs, 387 F.3d at 271
.
 72

    Id.
 73

    Id.
 74
    Id.
 75

    Id.
 76
    Id.
 77
    Id. at 277.
 78

    Id. at 276.
 79
    Id. at 275.
 80

    Id.
 81
    Id.
                               14
      2. 
Application of Clearly Established Law to Rosen
       Having reviewed the relevant Supreme Court law
through “a sharply focused lens[,]” we cannot conclude that
there is a directly applicable Supreme Court precedent that
would preclude the Commonwealth from using Rosen’s
statements against him at his second trial for the limited
purpose of impeachment.82 Rosen attempts to extrapolate a
principle of Fifth Amendment law from the similar yet
materially distinguishable cases we have just discussed.83
However, AEDPA’s deferential standard of review demands
more than this jigsaw approach. We therefore cannot find that
the Pennsylvania Supreme Court’s decision was either
“contrary to, or involved an unreasonable application of,
clearly established Federal law, as determined by the Supreme
Court . . . .”84

       The rule from Estelle—that a “criminal defendant, who
neither initiates a psychiatric evaluation nor attempts to
introduce any psychiatric evidence, may not be compelled to
respond to a psychiatrist if his statements can be used against
him at a capital sentencing proceeding”—is far too narrow to
help Rosen here.85 Rosen both initiated an evaluation and
introduced psychiatric evidence at his first criminal trial. It is
undisputed that the Commonwealth could compel Rosen to be
examined by its own expert for the purposes of preparing a
rebuttal in the first trial.86 The Estelle Court expressly


 82
    
Fischetti, 384 F.3d at 149
.
 83
    We reiterate that cases Rosen relies upon are materially
 distinguishable, such that we can identify discrete issues
 the Supreme Court has not yet addressed. It would not be
 enough to point to irrelevant or meaningless differences.
 See 
Matteo, 171 F.3d at 888 
(emphasizing that the
 petitioner is not required “to cite factually identical
 Supreme Court precedent”). The bar for relief under
 AEDPA is high but must not be insurmountable lest we
 effectively close the door to all relief on habeas. AEDPA
 requires that we defer, not that we abdicate.
 84
    28 U.S.C. § 2254(d)(1).
 85
    
Estelle, 451 U.S. at 468
.
 86
    A529 (“Federal courts have consistently reiterated . . .
 that when a defendant places his mental status at issue, his
                               15
acknowledged that “a different situation arises where a
defendant intends to introduce psychiatric evidence” and
expressed concern about the government’s ability to rebut such
evidence.87 Viewed through a “sharply focused lens,” Estelle
speaks only to the Fifth Amendment rights of someone who
never raises a mental health defense and not to the scope of the
Fifth Amendment waiver for someone, like Rosen, who raises
and presents an unsuccessful mental health defense that he later
abandons.88 The Pennsylvania Supreme Court could thus rely
on Commonwealth v. Boyle to find that the Fifth Amendment
waiver triggered by Rosen’s mental health defense at his first
trial extended to his second trial, at least with respect to the
issues raised by his own expert.89

       Buchanan is even less helpful to Rosen. There, the
defense had joined in the request for the psychiatric evaluation
and therefore the defendant’s statements did not result from an
involuntary examination. Rosen stresses the phrase “limited

 Fifth Amendment privilege against self-incrimination is
 not violated by a court-ordered psychiatric examination.”);
 see also 
Rosen, 42 A.3d at 996-97 
(discussing Morley and
 Sartin).
 87
    
Estelle, 451 U.S. at 472
; see also
 id. at 465 
(“When a
 defendant asserts the insanity defense and introduces
 supporting psychiatric testimony, his silence may deprive
 the State of the only effective means it has of controverting
 his proof on an issue that he interjected into the case.”).
 88
    Penry v. Johnson, 
532 U.S. 782
, 795 (2001) (noting that
 the Supreme Court has “never extended Estelle's Fifth
 Amendment holding beyond its particular facts”).
 89
    
447 A.2d 250 
(Pa. 1982). In Boyle, the Pennsylvania
 Supreme Court held that a defendant who testifies at his
 first trial waives his Fifth Amendment privilege and cannot
 reclaim it at a later trial on the same indictment, even
 where he declines to testify.
 Id. at 256. 
Without endorsing
 this decision or its application to Rosen, we merely note
 that the Pennsylvania Supreme Court could reasonably,
 even if incorrectly, determine that Rosen waived his Fifth
 Amendment privilege at his first trial by introducing expert
 psychiatric testimony regarding his mental health, and that
 this waiver transferred to his second trial despite the
 abandonment of his mental health defense.
                              16
rebuttal purpose” to conclude that “[t]he Buchanan [c]ourt
could avoid the Fifth Amendment problem only because of this
limitation on the use of such evidence.”90 Rosen therefore
proposes that Buchanan “clearly establishes” that psychiatric
evidence is only admissible to rebut the defendant’s mental
health defense. This inference is not supported by either the
text or reasoning of Buchanan. The Court explicitly stated that
the psychiatric evidence there was admissible “at the very
least” to rebut a mental health defense. The Court’s focus was
on the voluntary nature of the examination jointly requested by
the defense.91 Buchanan leaves open the scope of a Fifth
Amendment waiver triggered by a defendant’s mental health
defense. For example, Buchanan does not address what would
happen if the defense was raised and later abandoned, or
whether the waiver applies to involuntary examinations
compelled by the government.

       The most compelling Supreme Court support for
Rosen’s proposed principle of Fifth Amendment law comes
from Cheever. The reasoning in Cheever focuses on the
defendant placing his mental health at issue through his own
evidence, and the right of the prosecution to rebut such
evidence. The Supreme Court referred several times to the
evidence being admissible for the “limited purpose of
rebutting” the defense’s mental health defense. Citing to
Buchanan, the Court explained that it previously “held that
testimony based on a court-ordered psychiatric evaluation is
admissible only for a ‘limited rebuttal purpose.’”92

       According to Rosen, Cheever established that
compelled testimony from the government’s psychiatric expert
is only admissible to the extent it directly rebuts psychiatric

 90
    Rosen Br. 27.
 91
    
Buchanan, 483 U.S. at 422
; see also
 id. at 424 
(“Here, in
 contrast [to Estelle], petitioner's counsel himself requested
 the psychiatric evaluation . . . .”).
 92
    
Cheever, 571 U.S. at 97
; see also
 id. at 93-94 
(“The rule
 of Buchanan, which we reaffirm today, is that where a
 defense expert who has examined the defendant testifies
 that the defendant lacked the requisite mental state to
 commit an offense, the prosecution may present
 psychiatric evidence in rebuttal.”).
                              17
evidence presented by the defendant. Yet, even this narrow
reading of Cheever does not touch on several vital aspects of
Rosen’s case. Therefore, we cannot conclude that it clearly
established an applicable precedent. Cheever, for example,
does not address whether impeaching the defendant with
statements from the compelled exam, if he chose to testify,
would constitute a proper “rebuttal purpose.” In fact, Cheever
alluded to limitations on the Fifth Amendment protections for
testifying defendants.93 The Court further explained that
precluding the use of compelled psychiatric testimony “would
undermine the adversarial process, allowing a defendant to
provide the jury, through an expert operating as proxy, with a
one-sided and potentially inaccurate view of his mental state at
the time of the alleged crime.”94 These concerns about the
integrity of the judicial process and fairness to the government
undermine Rosen’s claim that he should have been allowed to
testify at his second trial without impeachment by his own
prior inconsistent statements. Nor does Cheever touch on
whether the proper admission of testimony for a “limited
rebuttal purpose” at one trial constitutes a Fifth Amendment
waiver in future proceedings where the mental health defense
is abandoned.95

        Given the limitations of AEDPA, the absence of
Supreme Court precedent addressing the use of compelled
statements given to the government’s mental health expert as
impeachment evidence is fatal to Rosen’s claim here. As we
have noted, the second trial court ruled that Rosen’s compelled
statements were inadmissible as substantive evidence and
admissible only for the limited purpose of impeachment in the
event Rosen testified. Estelle, Buchanan, and Cheever address
situations where the government sought to admit the

 93

    Id. at 94 
(“The admission of this rebuttal testimony
 harmonizes with the principle that when a defendant
 chooses to testify in a criminal case, the Fifth Amendment
 does not allow him to refuse to answer related questions on
 cross-examination.”).
 94

    Id.
 95
    See 
Boyle, 447 A.2d at 256 
(acknowledging that a
 defendant who testifies in one trial and thus waives his
 Fifth Amendment privilege cannot object to the admission
 of testimony at a later trial even where he does not testify).
                              18
defendant’s statements to prove or disprove a contested
issue—such as the defendant’s future dangerousness, intent, or
mental state. However, there was no indication in any of these
cases that the defendant intended to testify and was precluded
from doing so by the prospect of impeachment by compelled
statements.96 Therefore they do not address the admissibility of
a defendant’s statements for the purpose of impeaching the
defendant.

       Even Gibbs, with its otherwise striking factual
similarity to Rosen’s circumstances, is distinguishable on this
point. The testimony of the Commonwealth’s expert in Gibbs
was introduced “in the prosecution [case-in-chief]. . . simply to
repeat incriminating statements” made by the defendant and
offered “simply for the truth” of the matters asserted.97 In
contrast, Rosen’s second trial court specifically found that Dr.
Michals’ testimony was inadmissible in the case-in-chief and
would be allowed solely for the purpose of impeachment if
Rosen chose to testify. Impeachment evidence is not offered to
prove the truth of the matter asserted, but rather is offered to


 96
    Because we deny Rosen’s petition on other grounds, we
 do not reach the issue of whether the state court’s ruling on
 the motion in limine effectively denied Rosen his right to
 testify, or whether he forfeited his right to appeal the Fifth
 Amendment issue by electing not to testify. Compare Luce
 v. United States, 
469 U.S. 38
, 41-43 (1984) (holding that a
 defendant failed to preserve an issue for appeal where the
 trial court ruled that he could be impeached with a prior
 conviction under Fed. R. Evid. 609(a) and he thereafter
 declined to testify), with New Jersey v. Portash, 
440 U.S.
 450
, 454 (rejecting state’s claim that defendant’s Fifth
 Amendment challenge to the trial court’s ruling that his
 immunized testimony could be used as impeachment
 evidence is too “abstract and hypothetical” to review
 because defendant did not take the stand); and Brooks v.
 Tennessee, 
406 U.S. 605
, 612 (1972) (reviewing a state
 statute requiring a testifying defendant to testify first at his
 trial, despite the petitioner choosing not to testify because
 of the statute, and finding it violates the Fifth
 Amendment).
 97
    
Gibbs, 387 F.3d at 275
.
                               19
impugn the credibility of the person testifying.98 Moreover, the
jury can be specifically instructed that impeachment evidence
may be considered only for that limited purpose and cannot be
considered as substantive evidence of the defendant’s mental
state or intent.99

        The trial court’s ruling that Rosen’s statements could be
used only for impeachment is a material distinction on habeas
review under AEDPA. There is reason to believe that the
Supreme Court might treat impeachment by compelled
statements differently than the admission of such testimony as
substantive evidence in Rosen’s situation. In Harris v. New
York, the Supreme Court held that statements obtained in
violation of the Fifth Amendment under Miranda are still
admissible for the purposes of impeachment, even though such
statements are inadmissible as substantive evidence.100 The
Supreme Court explained that the right of the defendant to
testify “cannot be construed to include the right to commit
perjury[,]” and therefore “[h]aving voluntarily taken the stand,
[the defendant] was under an obligation to speak truthfully and
accurately, and the prosecution . . . did no more than utilize the
traditional truth-testing device[]” of impeachment by the
defendant’s own inconsistent statements.101 On the other hand,

 98
    Impeachment evidence, BLACK’S LAW DICTIONARY
 (11th ed. 2019) (“Evidence used to undermine a witness’s
 credibility.”).
 99
    Because Rosen elected a bench trial and chose not to
 testify, such an instruction was not necessary here.
 However, the possibility of giving such an instruction in a
 similar case is relevant to distinguishing between the use of
 evidence for substantive versus impeachment purposes. In
 addition, a judge at a bench trial would understand that she
 could not consider impeachment evidence for any purpose
 other than assessing a witness’s credibility.
 100
     Harris v. New York, 
401 U.S. 222
, 226 (1971) (“The
 shield provided by [Miranda] cannot be perverted into a
 license to use perjury by way of a defense, free from the
 risk of confrontation with prior inconsistent utterances.”).
 101

     Id. at 225; 
see also United States v. Havens, 
446 U.S.
 620
, 626 (1980) (explaining that “the deterrent function of
 the rules excluding unconstitutionally obtained evidence is
 sufficiently served by denying its use to the government on
                               20
coerced statements—such as where “the [speaker] is told to
talk or face the government’s coercive sanctions[]”—are
deemed involuntary and therefore inadmissible for any
purpose, including impeachment.102

        A court-ordered psychological or psychiatric exam, like
a custodial police interrogation, is an inherently coercive
situation. To the extent the District Court concluded that
Rosen’s “statements to Dr. Michals cannot be deemed
involuntary, coerced, or compelled since he voluntarily raised
the mental health defense[,]” we cannot agree.103 Rosen’s
statements, given while in custody, under court order, without
the benefit of Miranda warnings, are compelled testimony
under the Fifth Amendment.104 Nevertheless, whether

 its direct case” and therefore allowing the government to
 impeach a testifying defendant using evidence
 inadmissible in the case-in-chief).
 102
     
Portash, 440 U.S. at 459 
(holding that testimony given
 in response to a grant of legislative immunity is “coerced
 testimony” because the person must testify or potentially
 face contempt charges, and under such circumstances
 “there is no question whether physical or psychological
 pressures overrode the defendant’s will”); see also Kansas
 v. Ventris, 
556 U.S. 586
, 590 (2009) (“The Fifth
 Amendment guarantees that no person shall be compelled
 to give evidence against himself, and so is violated
 whenever a truly coerced confession is introduced at trial,
 whether by way of impeachment or otherwise.”); Mincey v.
 Arizona, 
437 U.S. 385
, 398-402 (1978) (holding that a
 statement taken from a defendant while he was
 hospitalized and in intensive care, slipping in and out of
 consciousness, and in “unbearable” pain was inadmissible,
 even for impeachment, because the statement was not “the
 product of his free and rational choice”).
 103
     Rosen, 
2018 WL 4030740
, at *1 n.1.
 104
     
Estelle, 451 U.S. at 467
, 469 (“The considerations
 calling for the accused to be warned prior to custodial
 interrogation apply with no less force to the pretrial
 psychiatric examination” because an examination “while in
 custody with a court-ordered psychiatric” expert is “not
 given freely and voluntarily without any compelling
 influences.”) (internal quotation marks and citation
                              21
testimony given to a psychiatrist under court order is “truly
coerced” and therefore involuntary, or merely compelled in the
same sense as a statement given to police in violation of
Miranda (and therefore still admissible for impeachment), is
yet to be determined by the Supreme Court.105

       Nor do we decide today whether Rosen’s statements
were voluntary or involuntary under the Fifth Amendment.
Rather, we merely conclude that the Pennsylvania Supreme
Court’s decision approving of the trial court’s admissibility
ruling is not contrary to or an unreasonable application of an
ambiguous area of Fifth Amendment law.106 This is not to say
that Rosen’s interpretation of the Fifth Amendment is not
plausible, or even compelling.107 However, such a rule is not

 omitted); see also 
Gibbs, 387 F.3d at 274 
(affirming that
 Miranda warnings apply to court-compelled psychiatric
 interviews). And unlike in the Miranda context, the only
 way Rosen could remain silent was to forfeit his mental
 health defense at trial. See 
Morley, 681 A.2d at 1258
, 1258
 n.5 (holding that a defendant who raises a mental infirmity
 defense “may not refuse to allow the Commonwealth
 psychiatrist to examine him or her on the basis that it
 violates the defendant’s privilege against self-
 incrimination” and “may be compelled to submit to a
 psychiatric exam”).
 105
     Compare 
Ventris, 556 U.S. at 590 
(“The Fifth
 Amendment . . . is violated whenever a truly coerced
 confession is introduced at trial, whether by way of
 impeachment or otherwise.”), and 
Portash, 440 U.S. at 458
 (distinguishing Harris because there the defendant made
 no claim that his statements obtained in violation of
 Miranda were coerced or involuntary), with 
Harris, 401
 U.S. at 224 
(admitting statement obtained in violation of
 Miranda for the purpose of impeachment where
 “[p]etitioner makes no claim that the statements made to
 the police were coerced or involuntary”).
 106
     See Mitchell v. Esparza, 
540 U.S. 12
, 17 (2003)
 (denying habeas petition where “precedent from [the
 Supreme] Court is, at best, ambiguous”).
 107
     Rosen Br. 31-32 (arguing that testimony a defendant is
 compelled to give to the government’s expert is admissible
 only for the limited purpose of rebutting a psychological
                             22
yet “clearly established.” Rosen’s credible argument about
where the Supreme Court should draw the line between cases
such as Harris and Portash does not satisfy the deferential
standard under AEDPA.108 It is not enough that Rosen’s
argument is persuasive; it must be required by law and the state
court’s contrary decision must not just be incorrect, but
unreasonable.109
    B. Because there is no clear Fifth Amendment
       violation, Rosen failed to demonstrate that he is
       entitled to relief under § 2254(d)(2).
      Rosen also argues that he is entitled to relief under 28
U.S.C. § 2254(d)(2) because the Pennsylvania Supreme
Court’s harmlessness analysis was based on “an unreasonable
determination of the facts in light of the evidence presented.”110


 defense and therefore inadmissible once that defense is
 abandoned, even for garden variety impeachment); see
 also 
Gibbs, 387 F.3d at 274 
(explaining that the Fifth
 Amendment waiver triggered by a mental health defense
 “is not limitless; it only allows the prosecution to use the
 interview to provide rebuttal to the psychiatric defense”).
 108
     Carey v. Musladin, 
549 U.S. 70
, 77 (2006) (holding that
 a state court’s decision is not contrary to or an
 unreasonable application of federal law where there is no
 Supreme Court holding that would require a different
 outcome).
 109
     
Matteo, 171 F.3d at 888 
(“[I]t is not sufficient . . . to
 show merely that [petitioner’s] interpretation of Supreme
 Court precedent is more plausible than the state court’s;
 rather, the petitioner must demonstrate that Supreme Court
 precedent requires the contrary outcome. This standard
 precludes granting habeas relief solely on the basis of
 simple disagreement with a reasonable state court
 interpretation of the applicable precedent.”); see also
 
Williams, 529 U.S. at 411 
(“[A] federal habeas court may
 not issue the writ simply because 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.”).
 110
     This claim was not raised in the District Court and we
 could therefore deem the argument waived. See Nelson v.
                               23
Rosen argues that the court improperly conflated the testimony
given to Dr. Fink with that given to Dr. Michals in concluding
that “the same admissions could have been established by
either expert’s testimony[.]”111 Based on that conclusion, the
Pennsylvania Supreme Court held that since Dr. Fink’s
testimony was indisputably admissible, “there is no reasonable
possibility that the error may have contributed to the
verdict.”112 However, Rosen is correct that there are significant
discrepancies between the statements that he gave to the two
experts. In fact, Dr. Michals testified to these discrepancies
during Rosen’s first trial in order to suggest that Rosen was
self-serving and challenge Rosen’s inconsistent version of
events.113 It is therefore unlikely that, if Rosen had testified,
“all of the impeachment evidence could have been elicited
solely from Dr. Fink, who was in possession of the same
mental health records and reports that Dr. Michals
possessed.”114

       Nevertheless, Rosen’s challenge to the harmlessness
analysis is predicated on a finding that there was indeed a Fifth
Amendment violation. Consequently, rebutting the state
court’s harmlessness analysis is a necessary but not sufficient
basis for relief. As we discussed above, we cannot conclude
that the Pennsylvania Supreme Court’s decision violated
Rosen’s clearly established Fifth Amendment rights. We
therefore need not delve into whether any such hypothetical
error was prejudicial to Rosen at trial.

IV.    CONCLUSION

 Adams USA, Inc., 
529 U.S. 460
, 469 (2000) (noting that
 “[i]t is indeed the general rule that issues must be raised in
 lower courts in order to be preserved as potential grounds
 of decision in higher courts”); Singleton v. Wulff, 
428 U.S.
 106
, 120 (1976) (noting that “[i]t is the general rule . . .
 that a federal appellate court does not consider an issue not
 passed upon below”). However, we can within our
 discretion choose to take up the issue on appeal and will do
 so briefly to dismiss the claim on the merits.
 Id. at 121.
 111
     
Rosen, 42 A.3d at 998
.
 112

     Id.
 11
3
     A149-50; Rosen Br. 35-40.
 114
     
Rosen, 42 A.3d at 997
.
                               24
      For the foregoing reasons, we will affirm the District
Court’s denial of the petition for habeas corpus.




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