Alfre Woodard is magnificent as a woman whose limits are tested, and then some, in “Clemency.”

Woodard plays Bernadine Williams, a prison warden, in writer and director Chinonye Chukwu’s gripping drama. As you watch, it may take a while to come around to it — the film, and Woodard’s performance, burn slowly but intensely throughout. It is a pleasure to watch.

OK, wait, “pleasure” might actually be the wrong word. It’s tough going at times. The film begins with the ice-cold Bernadine preparing for an execution, the 12th she’s overseen. She is all business as she prepares, so focused she doesn’t notice when a guard calls her a couple of times — at least not until he calls her “Bernadine.”

‘Clemency’: 3 out of 4 CST_ CST_ CST_ CST_ CST_ CST_ CST_ CST_ Neon presents a film written and directed by Chinonye Chukwu. Rated R (for some disturbing material, and language). Running time: 133 minutes. Now showing at local theaters.

The execution goes spectacularly wrong, a torturous exercise in human misery. Bernadine handles it as she handles everything — calmly, without emotion.

But the trips to the bar after work, and the difficulties with any kind of intimacy with her patient, and clearly long-suffering, husband, Jonathan (Wendell Pierce, also outstanding), suggest that more may be going on than she reveals to the world.

How could there not be?

Chukwu uses another death-row prisoner, Anthony Woods (Aldis Hodge, and this is a good place to say that all the acting is terrific), as the vehicle to show us Bernadine’s struggles.

Anthony is appealing his sentence, but Bernadine does not sugarcoat his prospects. There is a stunning scene in which she matter-of-factly discusses the details of his impending death with him — which drugs that take his life will do what, would he like witnesses, how would he like for them to dispose of the body — while he sits, stunned. It’s powerful stuff, made all the more so by Hodge’s simply sitting and staring in disbelief.

What a scene.

Equally devastating is a visit from Anthony’s old girlfriend (Danielle Brooks).

Anthony’s lawyer, Marty Lumetta (Richard Schiff, the picture of rumpled, put-upon frustration), has also worked too many of these cases to be optimistic. He will fight for Anthony, certainly. But you can tell by his posture, his look, his tone, that this is a block he’s been around many, many times, and he knows where the path leads. You want something good to happen for Anthony, even though we know little about his past.

This is not a film about guilt and innocence, at least not in the traditional way.

We don’t know whether Anthony committed murder. The issue is his current reality, and what, if anything, can be done to change it — if anything should be done.

Ultimately, though, it’s Bernadine’s journey, and Woodard’s film. It is a remarkable, open performance, revealing much about the character, but slowly, sometimes almost imperceptibly. She communicates so much with so little — a sigh, a look, a turn of her head. A tear can be devastating.

It should be. Woodard and Chukwu are getting at the value of a life, of many lives, and the toll that taking one can have on so many people. “Clemency” isn’t exactly a good time at the movies, but it’s definitely an enlightening one.