In the case of Lynaugh, Interim Director, Texas Department of Corrections v. Petty (1986), the U.S Supreme Court ruled in favor of Lynaugh and upheld a death sentence for Petty despite his claims that he was mentally ill at the time of committing murder. The court held that mental illness does not automatically exempt someone from capital punishment. It also rejected Petty's argument that executing him would violate his Eighth Amendment rights against cruel and unusual punishment because he had been diagnosed with paranoid schizophrenia after being sentenced to death. The court stated that it is up to each state to decide whether or not they want to execute people who are mentally ill, as long as their decision doesn't conflict with federal law.

In the dissenting opinion for Lynaugh v. Petty, Justice Thurgood Marshall argued that the majority's decision to uphold Petty's death sentence was a clear violation of his Eighth Amendment rights against cruel and unusual punishment. He contended that Texas' capital sentencing scheme failed to provide juries with adequate guidance on how to weigh mitigating factors in determining whether or not a defendant should be sentenced to death. This lack of guidance, he believed, created an unacceptable risk that juries would impose the death penalty arbitrarily and capriciously - thus violating defendants' constitutional rights. Furthermore, he criticized the majority for ignoring evidence suggesting racial bias in Texas' application of its capital sentencing laws.