In the case of Cary Michael Lambrix v. Harry K. Singletary, Jr., Secretary, Florida Department of Corrections (1996), Lambrix was a death row inmate who challenged his sentence on the grounds that he received ineffective assistance from his counsel during sentencing. He argued that his lawyer failed to investigate and present mitigating evidence about his background and mental health which could have potentially led to a lesser sentence. However, because Lambrix had previously filed habeas corpus petitions challenging other aspects of his conviction and sentence, this claim was considered an "abuse of writ" under federal law at the time - meaning it should have been raised in earlier litigation. The Supreme Court ruled against him by 5-4 majority vote stating that even if there were errors made by defense counsel during sentencing phase they did not undermine confidence in outcome since overwhelming aggravating factors existed for imposing death penalty; hence no prejudice resulted from alleged deficient performance by defense counsel as required for establishing ineffective assistance claim under Strickland v Washington standard.

In the dissenting opinion for Cary Michael Lambrix v. Harry K. Singletary, Jr., Justice Stevens argued that the Court's decision to deny review of Lambrix's case was a mistake due to its potential implications on capital punishment jurisprudence. He contended that there were two significant issues in this case: whether it is constitutional to execute someone who has been denied habeas corpus relief based on procedural default rules and whether such an execution would violate international law norms against arbitrary deprivation of life. Justice Stevens believed these questions deserved further examination by the court, particularly given their relevance to other death penalty cases across the country.