The unthinkably tough job of a prison warden (Alfre Woodard) who oversees executions is the subject of this delicate drama from writer/director Chinonye Chukwu (“alaskaLand”). Inspired by a true story, “Clemency” follows in the weary footsteps of Woodard’s Bernadine Williams, whom we meet as she’s supervising the lethal injection of a death row inmate whose procedure goes awry: The medic can’t find a viable vein, and the administration of lethal chemicals is botched, leading to a horrifying death while the prison staff slam shut the curtains so the invited attendees can’t witness what’s happening.

Shortly thereafter, execution looms for another inmate, Anthony Woods (Aldis Hodge), convicted of killing a policeman, and we watch as Bernadine’s longtime, steely dedication to her job begins to fray and unravel her marriage. Woodard gives a masterful performance (one in a career of many) as a woman in a position of relative power whose views on the morality of capital punishment aren’t allowed to come into play. She can only enforce the rules and treat her inmates as humanely as possible before supervising their deaths, a procedure that is clearly eroding her internally.

Chukwu’s screenplay follows Bernadine as the quiet, often inscrutable center of the hurricane of public opinion raging around Woods, who has become a media focus, but the rest of the cast is excellent, too. Hodge speaks volumes when he’s simply sitting wordlessly in his cell. Richard Schiff, as Anthony’s lawyer, is the public voice of capital punishment opposition as he pursues a last-minute pardon from the state. And Danielle Brooks of “Orange Is the New Black” is heartbreaking in a single scene as Woods’ visiting ex. “Clemency” is remarkable for the understanding it affords to all involved with its wrenching subject matter.