The U.S. Supreme Court won't consider an appeal that could have delayed an upcoming Tennessee execution.

The appeal involves Tennessee's midazolam-based lethal injection combination. Inmates claim in a lawsuit that the method causes excruciating pain.

RELATED: Supreme court rules death row inmate is not guaranteed a 'painless death'

RELATED: As U.S. executions wane, Tennessee moves to put more inmates to death

RELATED: There are fifteen East Tennesseans on death row

The appeal doesn't challenge lethal injection directly. Instead it challenges Tennessee secrecy laws surrounding the procurement of execution drugs. Inmates argue the laws prevented them from proving a more humane drug is available.

Justice Sonia Sotomayor agrees. In her dissent on Monday, she says the requirement that prisoners challenging one method of execution prove there is a better method available is "fundamentally wrong." She adds that state secrecy laws compound the injustice.

RELATED: I watched David Earl Miller die. Here is what I saw.

RELATED: Witness to an execution: The death of Billy Ray Irick

Don Johnson is scheduled to be executed Thursday for the 1984 murder of his wife, Connie Johnson.