The U.S. Supreme Court case Zant, Warden v. Stephens in 1981 revolved around the issue of whether a death sentence could be upheld if one of multiple statutory aggravating circumstances was invalidated on appeal. The defendant, Tony Mackall Stephens, had been convicted for murder and sentenced to death based on three aggravating factors under Georgia law: the crime was committed during an armed robbery; it involved torture; and he had prior convictions for capital felonies. On appeal, the Georgia Supreme Court found that one factor - involving torture - was unconstitutionally vague but affirmed his conviction by relying on remaining valid grounds. The U.S. Supreme Court held that even though one of these factors was invalidly applied to this case, as long as at least one legally sufficient aggravating circumstance remained after appellate review to justify imposing a death penalty under state law (which there were two), then such a sentence did not violate Eighth Amendment's prohibition against cruel and unusual punishment or Fourteenth Amendment's due process clause.

In the dissenting opinion for Zant, Warden v. Stephens, Justice William Brennan Jr., joined by Justice Thurgood Marshall, argued that Georgia's death penalty statute was unconstitutional because it allowed a jury to impose a death sentence based on an aggravating circumstance that had been declared invalid. They contended this violated the Eighth and Fourteenth Amendments' guarantees against cruel and unusual punishment and due process of law respectively. The justices believed that each aggravating circumstance should be valid in order to ensure fairness in capital sentencing decisions. They also expressed concern about arbitrariness in imposing the death penalty if juries were permitted to consider invalid factors as justification for such a severe punishment.