Lawyers on both sides of the Troy Davis case have until Wednesday to give a federal judge legal briefs.
After that, however, it's anyone's guess as to what might happen next.
The case is so unusual, legal experts disagree on what U.S. District Judge William Moore has the power to do.
Davis appeared before Moore at a hearing two weeks ago.
Davis' lawyers presented evidence they hope will exhonerate their client.
Professor Michael Mears of Atlanta's John Marshall Law School says, if judge Moore rules, Davis didn't meet a high bar of proving innocence, Davis surely will be executed.
"If he finds none of that evidence is clear and convincing to him, then I think the case is over for Troy Davis," Mears says. "I think the Supreme Court would simply dismiss the pending appeal."
Others believe the judge could recommend the court free Davis, who's on death row for the 1989 killing of Savannah police officer Mark MacPhail.
"If he were to find that all of this evidence is clear and convincing, or would have been clear and convincing, evidence, then I think the Supreme Court could order a new trial," Mears says.
His ruling could take weeks or months.