The U.S. Supreme Court case Lockhart, Director, Arkansas Department of Corrections v. McCree (1985) revolved around the issue of whether excluding jurors who would never vote for the death penalty in a capital punishment trial violates a defendant's Sixth Amendment right to an impartial jury. The respondent, William McCree Jr., was convicted and sentenced to life imprisonment without parole by an Arkansas court for first-degree murder. He appealed his conviction on grounds that his constitutional rights were violated when potential jurors opposed to capital punishment were excluded from serving on his jury during the guilt phase of his trial - creating what he termed as a "conviction-prone" jury. However, the Supreme Court ruled 6-3 against McCree stating that removing such individuals did not violate fair cross-section requirement nor create juries particularly prone towards conviction; hence it does not infringe upon defendants' Sixth Amendment rights.

In the dissenting opinion for Lockhart v. McCree, Justice Rehnquist argued that excluding jurors who would automatically vote against the death penalty does not create a conviction-prone jury and thus does not violate a defendant's Sixth Amendment right to an impartial jury. He contended that "death qualification" simply ensures that the jury is capable of fulfilling its duty under law, which includes considering capital punishment where appropriate. The majority's reliance on social science research was criticized as it did not provide definitive proof of bias in 'death-qualified' juries but merely suggested potential tendencies. Furthermore, he pointed out inconsistencies in applying this logic only to guilt determination phase and not sentencing phase of trials involving possible capital punishment.