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After his conviction by a Texas trial court for murder and the imposition of the death penalty, Jurek challenged the constitutionality of both his death sentence, alleging it was a "cruel and unusual" punishment, and the state's capital-sentencing procedure, alleging it would result in arbitrary and "freakish" imposition of the death penalty.

This case is one of the five "Death Penalty Cases" along with Gregg v. Georgia, Proffitt v. Florida, Roberts v. Louisiana, and Woodson v. North Carolina.

Is the death penalty a "cruel and unusual" punishment? Is Texas' capital- sentencing procedure unconstitutional?

The Court held that the death penalty was not per se a "cruel and unusual" punishment. Furthermore, the capital sentencing procedure in Texas was not unconstitutional on the theory that it would result in arbitrary and freakish impositions of the death penalty. While death penalty sentencing systems which permit juries to consider only aggravating, and no mitigating, circumstances are unconstitutional, Texas' sentencing system is not like this. Under its sentencing scheme, Texas juries may consider whatever evidence of mitigating circumstances there may be - thus allowing them to ponder not only why the death penalty should be imposed, but also why it should not. These options sufficiently focus the juries' attention on the defendant's unique circumstances and character, thus meeting constitutional requirements of particularity.