The Georgia and Florida victims were beheaded and all were killed in forested areas. The Florida Supreme Court heard Gary Hilton's appeal on Thursday in the death of Cheryl Dunlap.
The 46-year-old Crawfordville nurse was killed in north Florida's Apalachicola National Forest.
Hilton also is serving a life sentence in Georgia, where he pleaded guilty to killing 24-year hold Meredith Emerson of Buford, Ga.
He also pleaded guilty to ambushing and killing John and Irene Bryant, both in their 80s, while they were hiking in a national forest, in exchange for another life sentence.