The U.S. Supreme Court ruled that Kentucky's lethal injection is not cruel and unusual punishment and doesn't violate a person's 8th amendment rights.
Thursday in the Kentucky Supreme Court, John Palombi, the attorney representing Thomas Bowling and Ralph Baze is trying to argue a slightly different point.
He says the protocol for how a person on death row is actually killed should be made public and then be put up for debate.
Attorney's for the State Department of Corrections says the protocol is a private manner and there is no need for the public to be involved.
The Supreme Court also heard a separate case involving just Ralph Baze. That case had to do with the location of his trial.
It was originally set to begin in Franklin County, but at the request of the judge, it was moved to Rowan County.
At the time, neither side objected to the move, but now Baze's attorney says it was a violation of the judge's jurisdiction.
The state Supreme Court is now considering both cases.
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.