Amends the Federal judicial code to condition the consideration of writs of habeas corpus filed on behalf of individuals in custody under a State sentence of death upon a credible showing of innocence by affidavit or other instrument taken upon oath or affirmation. Specifies exceptions to such condition where the State: (1) does not provide by law for a right to appeal convictions resulting in death sentences and appellate review of death sentences; or (2) provides for such review but does not provide a procedure for collateral review of State proceedings resulting in death sentences.

Limits stays of execution granted for the purpose of making possible such required showing to 60 days (unless the applicant shows that a credible showing of innocence can be made but not within the time allotted).