In the 2003 case of David L. Nelson v. Donal Campbell, Commissioner, Alabama Department of Corrections et al., the United States Supreme Court addressed a dispute over whether an inmate's constitutional rights were violated when he was denied access to his preferred method of execution due to medical reasons. Nelson had been sentenced to death in Alabama and requested lethal injection as his method of execution; however, because he lacked accessible veins for this procedure due to past drug use, prison officials decided that they would have to cut into him surgically in order for it be carried out - a process known as "cut-down" procedure. Nelson argued that this constituted cruel and unusual punishment under the Eighth Amendment. The Supreme Court ruled unanimously in favor of Nelson on procedural grounds without addressing the substantive issue about what constitutes cruel and unusual punishment. The court held that federal courts should not dismiss lawsuits challenging methods of execution before plaintiffs have had an opportunity to gather evidence supporting their claims.

In the dissenting opinion for David L. Nelson v. Donal Campbell, Commissioner, Alabama Department of Corrections et al., Justice Stevens argued that the Court's decision to deny a stay of execution was incorrect due to unresolved issues in lower courts regarding Nelson's Eighth Amendment claim against lethal injection as cruel and unusual punishment. He contended that this case presented an opportunity for the court system to address these concerns before proceeding with capital punishment. Furthermore, he criticized the majority’s view on procedural default rules which prevented federal review of his claims because they were not raised at state level initially; stating it should be flexible enough to accommodate exceptions when compelling reasons exist such as potential violation of constitutional rights or fundamental fairness principles. In essence, Justice Stevens believed that by denying a stay and allowing execution without addressing these significant legal questions undermined public confidence in justice administration.