Listen to Episode 11 of Slate’s Amicus:

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Last month, the Supreme Court agreed to hear Glossip v. Gross, an Eighth Amendment challenge to the way Oklahoma executes its capital defendants. Just a few days earlier, the court had allowed one Oklahoma execution to go forward, before deciding to hear the case and then halting three others. Adding to the confusion is the fact that a mere seven years ago, the court ruled in Baze v. Rees that Kentucky’s lethal injection protocol was not cruel and unusual.

So what’s changed? On this episode of Amicus, Dahlia puts that question to two experts—professor Deborah Denno of Fordham University School of Law, and Dr. Joel B. Zivot, an anesthesiologist and instructor at Emory University Hospital. Together they sort through how lethal injection has been administered in recent years, what the court might be thinking as it agrees to revisit the issue, and whether states’ capital punishment system can be repaired.

This week’s excerpts from the Supreme Court’s public sessions were provided by Oyez, a free law project at the Chicago-Kent College of Law, part of the Illinois Institute of Technology.

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This week’s episode is sponsored by The Great Courses. Save up to 80 percent off their most best-selling courses when you visit http://thegreatcourses.com/Amicus. We’re also sponsored by HBO. Its new documentary series The Jinx: The Life and Deaths of Robert Durst airs Sundays at 8 on HBO, starting this Sunday, Feb. 8.

Podcast production by Tony Field.