In the case of Ronald Dean Lowe v. Marcus Pogue et al., 1998, the U.S Supreme Court dealt with issues related to habeas corpus petitions and procedural default rules. Ronald Dean Lowe was convicted for murder in Tennessee state court and sentenced to death. He appealed his conviction on grounds that he received ineffective assistance from his counsel during trial but failed to raise this issue at every level of state review process which led to a procedural default under Tennessee law. The federal district court denied relief, agreeing with the State's argument that Mr. Lowe had procedurally defaulted on his claim by failing to present it in state proceedings as required by law. On appeal, however, the Sixth Circuit Court reversed this decision stating that Mr.Lowe could overcome procedural default if he demonstrated cause and prejudice or a fundamental miscarriage of justice exception applied due its actual innocence claim. The Supreme Court disagreed with Sixth Circuit’s interpretation regarding exceptions applicable for overcoming procedural defaults especially when there is no new evidence supporting claims of actual innocence presented after trial verdicts are rendered. Therefore,the Supreme Court held that an actual-innocence claim does not constitute an exception allowing federal courts' consideration of procedurally defaulted claims unless petitioner supplements such claims with new reliable evidence—whether it be exculpatory scientific evidence trustworthy eyewitness accounts or critical physical evidence—that was not presented at trial.

In the dissenting opinion for Ronald Dean Lowe v. Marcus Pogue et al., Justice Stevens argued that the majority's decision to deny a habeas corpus petition based on an alleged violation of Miranda rights was incorrect. He contended that the petitioner, Mr. Lowe, had not been adequately informed of his right to remain silent and have counsel present during questioning by police officers following his arrest for murder charges in 1981. According to Justice Stevens, this constituted a clear violation of Miranda rights which should have resulted in suppression of any statements made by Mr. Lowe during interrogation without legal representation present or after he expressed desire to remain silent until having consulted with an attorney.