On Thursday, the Kentucky Supreme Court will hear arguments from two inmates on death row.
Thomas Clyde Bowling Junior, is suing the Kentucky Department of Correction.
Ralph Baze is suing the state.
The hearing comes six months after the U.S. Supreme Court struck down Bowling and Baze's argument that lethal injection is cruel and unusual punishment.
Bowling is awaiting execution for the 1990 murders of a Lexington couple outside their dry cleaning business.
Baze killed the Powell County Sheriff and a deputy in 1992.