LITTLE ROCK — A day after court rulings halted the scheduled executions of Don William Davis and Bruce Earl Ward, Arkansas continued Tuesday to fight court challenges by attorneys for the five remaining death-row inmates scheduled to be executed this month.

Late Monday night, the U.S. Supreme Court upheld the Arkansas Supreme Court’s stay of the executions of Davis and Ward, who had been set to die that evening. The men claim they were denied access to independent mental health experts and that their executions should be delayed while the U.S. Supreme Court considers a case involving the same issue.

In February, Gov. Asa Hutchinson scheduled eight executions over an 11-day span this month, seeking to use the state’s supply of one of its execution drugs before it expires at the end of April.

In addition to Davis and Ward, Jason McGehee has been removed from the schedule because a federal judge stayed his execution after the state parole Board recommended he receive executive clemency.

The five men who still have April execution dates are Ledell Lee and Stacey Eugene Johnson, who are scheduled to die Thursday; Marcell Wayne Williams and Jack Harold Jones, who are scheduled to die Monday; and Kenneth Williams, who is scheduled to die April 27.

An attorney for Lee argued unsuccessfully Tuesday in Pulaski County Circuit Court that Judge Herbert Wright should order new DNA testing of evidence — a hair and blood on a shoe — that contributed to Lee’s conviction in the 1993 beating death of 26-year-old Debra Reese of Jacksonville in her home.

Attorney Lee Short told Wright that current DNA testing is much more advanced than the testing that was available decades ago. He said the case has similarities to that of the men known as the “West Memphis Three,” Damien Echols, Jason Baldwin and Jessie Misskelley, who were convicted in the 1993 killings of three boys in West Memphis but were able to secure a plea deal that freed them in 2011 after their lawyers obtained new DNA testing of evidence.

“Those individuals are walking free men today, and it’s because of those tests,” Short said.

Wright denied the request for new tests, saying in a written order there was sufficient evidence aside from the hair and the blood to support Lee’s conviction, including witnesses’ testimony.

“The verdict has been attacked, appealed and considered multiple times here and in higher courts, and this court will not now substitute its own judgment for that of the jurors of decades removed,” Wright said in his order.

Also Tuesday, U.S. District Judge Kristine Baker dismissed a challenge by Johnson to the state’s lethal-injection protocol.

Johnson’s lawyers argued in court filings the three-drug cocktail the state intends to use in executions is especially likely to result in severe pain to Johnson because he suffers from multiple health conditions, including hypertension, angina and probable heart and lung disease.

Baker wrote in her order dismissing Johnson’s suit that he showed no reason why he could not have presented his claim sooner.

Johnson is sentenced to die for the 1993 slaying of Carol Jean Heath of De Queen.

In another development Tuesday, Baker cancelled a hearing in a challenge to the lethal-injection protocol by Marcell Williams.

Williams’ attorneys argued in court filings the three-drug cocktail is especially likely to result in severe pain to Williams because he is obese and has diabetes, high cholesterol and high blood pressure.

Baker ordered Williams to show why his suit should not be dismissed based on the fact he could have presented his claim sooner. In a response filed Tuesday afternoon, Williams’ attorneys said his physical condition is “constantly evolving and worsening as he ages and deteriorates in solitary confinement.”

Williams is sentenced to die for the 1994 killing of 22-year-old Stacy Errickson of Jacksonville.

Also Tuesday, medical supply company McKesson Medical-Surgical refiled a lawsuit that was dismissed over the weekend, without prejudice, alleging that Arkansas obtained one of its execution drugs from the company improperly.

Before the original version of the suit was dismissed, Pulaski County Circuit Judge Wendell Griffen issued a temporary restraining order in the case that would have blocked the state from using the drug in executions. Later the same day, Griffen took part in an anti-drug penalty protest outside the Governor’s Mansion, which prompted the Arkansas Supreme Court to bar Griffen from presiding over cases involving the death penalty.

Attorney General Leslie Rutledge filed a motion Tuesday seeking to have the new version of the suit moved to Faulkner County Circuit Court.