[1] The Supreme Court held that not considering a defendant's low IQ would breach his Eighth Amendment rights and constitute a cruel and unusual punishment.

[2] The District Court for the Southern District of Texas denied Tennard a certificate to appeal on the basis that a low IQ is not a sufficient reason for appeal there was no evidence presented that Tennard's behavior was mentally retarded and that mental retardation was related to the criminal act.

The main issue the U.S Supreme Court considered was whether the Fifth Circuit improperly denied Mr. Tennard's certificate of appeal since he had presented substantial evidence of a violation of his constitutional rights, or had "demonstrated that reasonable jurists would find the district court's assessment of the constitutional claims debatable or wrong?"

If the jury is not instructed to consider all relevant mitigating factors, the defendant's Eighth Amendment rights are violated as failure to do so constitutes cruel and unusual punishment.

[3] The case formed part of a series of decisions in which the Supreme Court adjusted and refined the capital sentencing methods of the various states.