Cite as: 507 U. S. 680 (1993)
Opinion of O'Connor, J.
ante, at 686, that inform our habeas jurisprudence counsel the exclusion of Miranda claims just as strongly as they did the exclusionary rule claims at issue in Stone itself.
II
In Stone, the Court explained that the exclusionary rule of Mapp v. Ohio, 367 U. S. 643 (1961), was not an inevitable product of the Constitution but instead " 'a judicially created remedy.' " Stone, supra, at 486 (quoting United States v. Calandra, 414 U. S. 338, 349 (1974)). By threatening to exclude highly probative and sometimes critical evidence, the exclusionary rule "is thought to encourage those who formulate law enforcement policies, and the officers who implement them, to incorporate Fourth Amendment ideals into their value system." Stone, 428 U. S., at 492. The deterrent effect is strong: Any transgression of the Fourth Amendment carries the risk that evidence will be excluded at trial. Nonetheless, this increased sensitivity to Fourth Amendment values carries a high cost. Exclusion not only deprives the jury of probative and sometimes dispositive evidence, but also "deflects the truthfinding process and often frees the guilty." Id., at 490. When that happens, it is not just the executive or the judiciary but all of society that suffers: The executive suffers because the police lose their suspect and the prosecutor the case; the judiciary suffers because its processes are diverted from the central mission of ascertaining the truth; and society suffers because the populace again finds a guilty and potentially dangerous person in its midst, solely because a police officer bungled.
While that cost is considered acceptable when a case is on direct review, the balance shifts decisively once the case is on habeas. There is little marginal benefit to enforcing the exclusionary rule on habeas; the penalty of exclusion comes too late to produce a noticeable deterrent effect. Id., at 493. Moreover, the rule "divert[s attention] from the ultimate question of guilt," squanders scarce federal judicial re-
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