In the case of Dennis Sochor v. Florida, 1991, the US Supreme Court ruled on whether a jury instruction regarding an aggravating factor in a death penalty case violated the Eighth Amendment's prohibition against cruel and unusual punishment. The defendant, Dennis Sochor was convicted for first-degree murder and sentenced to death by a Florida court. During sentencing, one of four aggravating factors considered was later found invalid by the state supreme court but it upheld his sentence stating that other valid factors were enough to justify capital punishment. However, Sochor appealed arguing this constituted "harmless error". The U.S Supreme Court disagreed with him ruling that such an approach could not be applied when dealing with constitutional errors at capital sentencing proceedings because it would require speculation about how jurors might have weighed various factors if they had been properly instructed. Therefore, it held that using an invalid or improperly defined aggravating circumstance in weighing towards a decision for death penalty is not harmless error under Eighth Amendment standards.

In the dissenting opinion for Dennis Sochor v. Florida, Justice John Paul Stevens argued that the majority's decision to uphold Sochor's death sentence despite acknowledging constitutional error in his sentencing was fundamentally flawed. He contended that the jury had been improperly instructed on an "especially heinous, atrocious or cruel" aggravating factor and this could have influenced their decision to recommend a death sentence. Furthermore, he disagreed with the majority’s application of harmless-error analysis as it presumed what a hypothetical jury might decide rather than focusing on what actually occurred during trial proceedings. The justice also criticized Florida Supreme Court’s reweighing process which upheld Sochor’s death penalty without considering whether improper instructions affected original verdicts. For him, these errors were not trivial but substantial enough to warrant reversal of conviction or at least remand for resentencing.