The premise of “Precious” is so unsettling and bleak that no one would blame you if you didn’t want to see it: It’s the story of an obese 16-year-old illiterate Harlem girl who’s pregnant (for the second time) by her own father, lives with her monstrously abusive mother, and has almost given up on life. But if you do see it, you’ll find that it’s compelling and artistic, punctuated with warm humor and masterful performances, and ultimately triumphant and hopeful.

The girl is named Claireece “Precious” Jones (she goes by Precious), and she’s played with astonishing rawness by newcomer Gabourey Sidibe. Narrating the film, Precious tells us the grim facts. Beyond the ones already noted, she is still in junior high school (where she’s dumbly in love with her kindly math teacher); her first child, born with Down syndrome, is technically in her mother’s custody but is actually cared for by her grandmother; and her mother, Mary (Mo’Nique), is a welfare-absorbing harridan who abuses Precious in every possible way, hating her daughter for “stealing” her man. Precious did no such thing, of course — she was raped by her father — but Mary is not interested in details.

Precious is directed by her principal to an alternative school called Each One Teach One. Her class is populated by other girls who dropped out or were kicked out of public schools for various reasons; it’s telling that even in such a motley group, Precious is still the most timid, the most withdrawn, and the most messed-up. The teacher, Ms. Rain (Paula Patton), is dedicated to her work, perhaps the first adult to ever take a genuine interest in helping Precious. The other students might be Precious’ first friends, too.

Sapphire, the pen name of a New York poet who has worked with at-risk teens like those in the book, published her novel, called “Push,” in 1996, and it’s taken this long for someone to figure out how to film it. (It premiered at Sundance under the title “Push: Based on a Novel by Sapphire,” but was changed to Precious to avoid confusion with the other 2009 film called “Push.”) That someone is Lee Daniels, who produced “Monster’s Ball” and “The Woodsman,” so he’s pretty well-versed in harrowing subject matter. I didn’t see his directorial debut, “Shadowboxer” (I understand it has scenes of Cuba Gooding Jr. doin’ it with Helen Mirren), but “Precious” is an impressive sophomore effort. Daniels (working from a screenplay by first-timer Geoffrey Fletcher) directs boldly and confidently, never exploitative of the film’s subject matter, never wallowing in the depravity, yet not overly cautious or safe, either. Nothing is watered down. He shows us as much as we need to see, artfully conveying Precious’ stark situation without fixating on the sordid details. It helps that Precious tends to retreat into her imagination, giving Daniels a way to rescue us from the situation, too.

Sidibe’s performance as Precious is fantastic — fully realized, perfectly authentic, and without a hint of contrivance. It’s the sort of debut that will either be followed by a stellar career, or that she’ll never be able to live up to. I hope we get a chance to see what else she can do. Meanwhile, there are eye-opening turns by Mo’Nique, who helps us understand Precious’ mother’s frame of mind without making her sympathetic; and Mariah Carey, who’s almost unrecognizably un-glamorous as a social worker.

Precious, in addition to her physical problems, lacks even basic self-esteem, and the film is largely about her journey toward normalcy. Things will never be super-awesome for her; the point is that she can learn to cope with life and find a semblance of happiness and self-respect. She sums up her attitude thus: “The other day, I cried. I felt stupid. But you know what? F*** that day.” That day is gone. What happens today and tomorrow is what’s important. That feeling of hopefulness, not the awfulness that precedes it, is what you’ll take with you when the film is over.

A- (1 hr., 45 min.; R, pervasive harsh profanity, brief strong sexuality, some violence, intense themes.)