In the case of Barefoot v. Estelle, 1982, Thomas Andy Barefoot was convicted for murder in Texas and sentenced to death. He appealed his sentence on the grounds that psychiatric testimony regarding his future dangerousness was admitted during sentencing despite its unreliability. The Supreme Court ruled against him with a vote of 6-3, stating that such evidence could be used if it met certain standards of reliability under Texas law. Furthermore, they held that federal courts should not issue stays of execution on the basis of challenges to state court decisions unless there is reasonable doubt about their correctness or an absence of adequate opportunity for full and fair litigation at the state level.

In the dissenting opinion for Barefoot v. Estelle, Justice Blackmun argued that the majority's decision to allow psychiatric predictions of future dangerousness in capital sentencing hearings was fundamentally flawed and unjust. He contended that such predictions are inherently unreliable due to their speculative nature and high potential for error, which is unacceptable given the irreversible consequences of a death sentence. Furthermore, he criticized the majority's dismissal of empirical studies demonstrating this unreliability as irrelevant or inconclusive. Additionally, he expressed concern over allowing juries to make life-or-death decisions based on such dubious evidence without providing them with clear instructions or standards regarding its use and interpretation. This lack of guidance could lead to arbitrary and inconsistent application of the death penalty across cases - an outcome incompatible with principles of fairness and justice.