The case before the court involves Paul Gregory House, who was convicted in the July 1985 abduction, attempted rape and murder of Carolyn Muncey, a young mother of two, in Union County, Tenn., north of Knoxville.
House, who was on parole for a sex offense in Utah at the time, was convicted and sentenced to death.
Twenty years later, DNA tests, not available at the time of House's conviction, revealed that semen found on Muncey's nightgown and underwear belonged to her husband.
But the justices didn't focus on the DNA evidence until the end of the hour-long argument. Chief Justice John Roberts, in an exchange with Tennessee's lawyer, stressed that the justices aren't being asked to second-guess the jury that convicted House.
Instead, Roberts said, the justices are looking at "the standard of review question" for lower courts to determine how to weigh new evidence of innocence.
"This is another opportunity for the justices to define and to refine procedural rules in death penalty cases in ways that would directly impact the lives of capital defendants," says CBSNews.com Legal Analyst Andrew Cohen. "The court here has to decide how receptive federal and state lower courts ought to be to the use of DNA evidence after a conviction to try to establish the convict's innocence."
For most of the session, Justice Antonin Scalia, a proponent of curbing endless inmate appeals, steered the argument toward the strongest piece of evidence remaining against House: spatters of the victim's blood found on the defendant's jeans.
"I agree it would have been a much closer case," Scalia said, had the DNA results been available at trial. "But once a case has been tried ... we have a much different test. And that is whether any reasonable juror would have found him guilty. That is a very heavy burden."
In recent years, as scientific testing of biological materials left at crime scenes has improved, exonerations of death-row inmates have increased, raising concerns among civil libertarians and prosecutors that an innocent person could be executed, or already has been.