A tug-of-war between faith and science is at the heart of John Pielmeier’s Agnes of God, a hit play steeped in mystery. First produced at the Humana Festival of New American Plays in 1980, the drama went on to become a Broadway hit and a movie. Now Miami’s New Theatre has revived it, dubbing the three-character piece an American classic.

That description is an overreach. Agnes of God is an intriguing play, one that can be thought-provoking, touching and disturbing. But more than three decades after it first hit the stage, the celebrated drama also reveals its flaws, at least in the New Theatre production.

Staged and designed by artistic director Ricky J. Martinez, Agnes of God features a trio of strong South Florida performers: Pamela Roza as psychiatrist Martha Livingstone, Barbara Sloan as Mother Miriam Ruth and Christina Groom as Agnes, a novice nun accused of murdering her newborn baby. (Yes, you read that right.)

Pielmeier makes the two older women, each wanting to help Agnes in her own way, opponents.

Dr. Livingstone is a court-assigned shrink tasked with trying to determine Agnes’ sanity as she gets to the bottom of the case: How did Agnes get pregnant? Who knew about her condition? Was Agnes alone when she gave birth? Did she or someone else wrap the umbilical cord around the baby’s neck and hide the body in a wastebasket?

The Mother Superior describes Agnes as “fragile” and “different.” She treasures the young woman who sings, she says, with the voice of an angel. Miriam Ruth is most anxious to protect Agnes and her intensely devout faith, and she hopes that the justice system will somehow allow Agnes to remain with her contemplative order of nuns.

As for Agnes, she has psychologically shut down any memory of pregnancy, birth or infanticide. She is clearly naive, debatably an innocent. And as the play progresses, it becomes clear that Agnes — sweet, frightened Agnes — is a deeply disturbed victim of abuse.

Pielmeier layers secrets, twists and less-than-compelling motivational factors into the script. Some deficiencies can be glossed over by bravura acting, but the New Theatre cast doesn’t rise to that level.

Martinez gets solid performances from all three women, but Roza has a tough time making Dr. Livingstone’s back story compelling, Sloan can’t disguise the ridiculous nature of some of the older nun’s pronouncements, and Groom (who is clearly not the kid Agnes is meant to be) has a rough time with Agnes’ more unhinged speeches. She does, however, have a lovely singing voice that adds immeasurably to the production.

Agnes of God swings from whimsy to horror, religious ecstasy to physical and psychological degradation. It’s a carefully constructed piece of theater, sometimes effective, at other times ludicrous. But overall? It’s no great American play.