What is the test for admitting or denying evidence that other parties were involved in the crime?

"Fundamental standards of relevancy, subject to the discretion of the court to exclude cumulative evidence and to insure orderly presentation of a case, require the admission of testimony which tends to prove that a person other than the defendant committed the crime that is charged." United States v. Armstrong, 621 F.2d 951, 953 (9th Cir.1980). See also United States v. Stewart, 770 F.2d 825, 830 (9th Cir.1985) ("A defendant is entitled to prove his innocence by showing that someone else committed the crime."), cert. denied, 474 U.S. 1103 (1986).