In the 1983 case Maggio, Warden v. Williams, the United States Supreme Court ruled in favor of the petitioner, reversing a decision by lower courts to stay an execution. The respondent had been convicted of murder and sentenced to death but argued that his constitutional rights were violated because he was not allowed to present mitigating evidence during sentencing. However, this claim was only raised after several rounds of appeals and habeas corpus petitions had already been denied on other grounds. The Supreme Court held that procedural default rules prevented consideration of this new claim because it could have been raised earlier in state court proceedings but wasn't. Therefore, even if there might be merit to the argument about mitigating evidence (which they did not decide), it was too late for him to raise it now.

In the dissenting opinion for Maggio, Warden v. Williams, Justice Brennan disagreed with the majority's decision to reverse a stay of execution granted by lower courts on grounds that it was procedurally flawed. He argued that this case raised serious constitutional questions about whether an inmate could be executed while his habeas corpus petition was still pending in federal court. In addition, he expressed concern over the potential violation of Eighth Amendment rights if an individual were to be executed without having their claims fully heard and adjudicated. Brennan also criticized the majority for not providing clear guidance on how lower courts should handle such cases in future, thereby potentially causing confusion and inconsistency in death penalty litigation.