Clarence Hill was sentenced to death in Florida, which ordinarily uses a three-drug combination for executions. Hill claimed that this particular form of lethal injection was unnecessarily and gratuitously painful, and that it therefore violated the Eighth Amendment's prohibition on cruel and unusual punishment. However, Hill had previously filed for a federal writ of habeas corpus challenging his conviction, and the federal district court ruled that his new challenge was the practical equivalent of a second habeas corpus appeal. Successive habeas corpus appeals are not allowed under 28 U.S.C. 2244, and so the district court rejected Hill's petition. The Eleventh Circuit Court of Appeals affirmed the decision.
https://www.oyez.org/cases/2005/05-8794