The 10th U.S. Circuit Court of Appeals in Denver denied Carl Case's appeal on February 26th.
Case was sentenced to life in prison plus 18 years after he was convicted of the 1982 murder and rape of Nancy Mitchell.
The teenager's body was found in a dam outside Carlsbad.
In his appeal, Case had claimed there was new and previously undisclosed evidence regarding a trial witness.
Case also claimed that two prosecution witnesses had recanted their trial testimony.
However the 10th U.S. Circuit Court of Appeals ruled that Case received a fundamentally fair trial.
Justices also ruled that Case's due process rights weren't violated in his appeal, and that the newly discovered evidence doesn't require a new trial.