A comedy about mental illness is hard to get right. It’s all too easy for filmmakers to trivialize real problems like bipolar disorder by turning them into collections of adorable quirks. But if they take an earnest, politically correct route, where are the laughs? With Silver Linings Playbook (opening in Vermont on December 25), writer-director David O. Russell walks a fine line between those two pitfalls and generally keeps his balance. The result is a romantic comedy for people who don’t like what Hollywood has been calling “romantic comedies” these days.

Like the screwball comedies of yore, Silver Linings Playbook, based on Matthew Quick’s novel, is almost frenetically verbal. The frenzied pace and rhythms of the dialogue generate much of the humor, but they also reflect the perilously manic side of protagonist Pat Solitano (Bradley Cooper).

Pat — a thirtysomething who, at the film’s opening, comes to live with his parents in suburban Philadelpha — has no social filters. Like many cinematic manchildren, he’s incapable of tact or subterfuge, bursting with adolescent enthusiasms, but the problems he faces are adult ones. Pat is fresh from eight months in a mental institution, where he landed as part of a plea bargain after brutally assaulting his wife’s lover. He’s convinced that all he needs to do to win his wife back is prove himself a changed man.

Armed with this delusion, Pat is sweet, funny and, at times, downright scary, and Cooper does justice to all those aspects. From an actor who has been sleepwalking through his dramatic roles (though showing more liveliness in comedies), it’s a revelatory performance.

Russell, whose specialty is voluble, screwed-up families (see: The Fighter), surrounds Pat with characters who remind us that mental illness is a spectrum, not an either/or. There’s his dad (Robert De Niro), a bookie whose ritualistic Eagles fandom easily qualifies as obsessive compulsion; his mom (Jacki Weaver), who enables her husband with game-day treats; and his best friend (John Ortiz), a model suburban dad on the verge of a nervous breakdown. But it’s not till Pat encounters Tiffany (Jennifer Lawrence), a young widow who shares his tendency to blurt out and act out, that he meets his match.

Given her youth, Lawrence’s casting seems questionable on paper; the role clearly calls for a woman who has lived, if not matured. That’s exactly how Lawrence plays it, without a hint of ingenue. Tiffany has Pat’s number immediately, and as she pursues him — over his protestations of eternal love for his estranged spouse — the movie’s central question becomes: Can two troubled people learn to live with each other’s “issues,” perhaps even to love each other?

In its second half, Russell engineers a conflict that sends the movie toward something approximating a crowd-pleasing Hollywood finish. That climax — yes, it involves a dance-off — feels a touch too forced to be entirely satisfying, but it doesn’t damage a film whose real pleasures lie in getting to know these impulsive, imperfect characters.

Would viewers relate as easily to Pat and Tiffany if attractive movie stars weren’t playing them? Or would we focus solely on their dysfunction? (Todd Solondz’s recent Dark Horse offers an alternative, almost unbearably grim vision of how a romance between two emotionally disturbed people might look.) It’s hard to say. But the whole movie has an infectious vitality tempered with realism, much like Pat’s not-too-optimistic personal credo: “If you stay positive, you have a shot at a silver lining.”