Here are a list of precedents for the case.
Furman v. Georgia (1972): The Court invalidated death penalty laws since they violated the Amendment against cruel and unusual punishment in leaving too much discretion to juries in imposing this ultimate penalty.
Gregg v. Georgia (1976): The Court refused to outlaw capital punishment. The Court refused to declare the death penalty unconstitutional under all circumstances (especially in murder cases).
Weems v. U.S. (1910): The Court recognized that the constitutional prohibition against cruel and unusual punishment is not fastened to the obsolete but may acquire meaning as public opinion becomes enlightened by a humane justice.
Woodson v. North Carolina (1976): The Court invalidated a mandatory capital sentencing system since the Eighth Amendment recquires consideration of the character and record of the individual offender and the circumstances of the particular time.
Ford v. Wainwright (1986): The Court prohibited the execution of prisoners who are insane.
Caldwell v. Mississippi (1985): A death sentence must be struck down when the circumstances under which it has been imposed create an unacceptable risk that the death penalty may have been meted out arbitrarily or capriciously or through whim or mistake.
Lee v. Washington (1968): Equal protection is not denied to persons convicted of crimes.