TALLAHASSEE, Fla. -

The Florida Supreme Court on Monday rejected an 11th-hour appeal from Death Row inmate Eddie Wayne Davis, who is scheduled to be executed Thursday for the murder of an 11-year-old girl in Polk County.

Davis argued, in part, that he suffers from a medical condition that could make the state's lethal-injection process unconstitutional in his case. The issue centered on the state's use of midazolam hydrochloride in a three-drug lethal injection cocktail.

Davis contended that the drug might not work as expected because he suffers from a condition known as porphyria. But the Supreme Court rejected that argument, saying Davis "has not met his 'heavy burden' to show that the injection of midazolam in the amount prescribed by the lethal injection protocol will not render him unconscious and insensate before he suffers any of the effects of a possible porphyria attack."

Davis, 45, was convicted of kidnapping 11-year-old Kimberly Waters, sexually assaulting and strangling her and leaving her body in a dumpster in 1994.