Tim Burton and the Farrelly brothers try to grow up.

"Maturity" is a double-edged ideal for some movie directors, especially the ones who start out dark and punky and make a lot of noise about breaking the rules. You want them to evolve as artists and to attain self-knowledge as human beings, of course. You want them to be happy. You just don't want them to confuse their hunger for mainstream acceptance (and its attendant gold statuettes) with artistic growth. You don't want them to think that some piece of whorishly life-affirming swill is the best and noblest work of their careers.

Stuck on You (20^th Century Fox) and Big Fish (Columbia Pictures) are two new heart-tuggers by three of our cinema's bad boys, two of them joined at the hip: the team of Peter and Bobby Farrelly, and Tim Burton. Both movies are emotional leaps for their makers, but only the Farrellys seem to have found a fertile middle ground between their new maturity and their blessedly infantile roots.

The brothers, of course, exploded onto the scene like a popped whitehead with Dumb & Dumber (1994), and that title has become a kind of shorthand both for their comedies and for the people who flock to them. I'll concede that their movies are broadly written and that they've never learned the niceties of composition or staging. I'll concede that many of their plots feature cretinous males, unable to control their bodily fluids, pursuing silky blondes like Cameron and Gwyneth—not exactly progressive territory. But I consider the Farrellys the most compassionate filmmakers in Hollywood. Guerrilla humanists, they work in the lowest and most infantile of genres with disarming moral authority.

From their earliest work they had a love not just for dense or downright moronic heroes, but also for the mentally and physically challenged (or disabled, or whatever). "What a terrible thing, to exploit people with learning disabilities or spina bifida for laughs!" railed many critics, ignoring that the Farrellys' proportion of empathy to mockery was about 80-20, that their underlying impulse was a therapeutic one (to make the disabled part of the same continuum as the rest of us poor fools), and that these non-actors (many of them friends of the directors) were plainly having the time of their lives.

In Stuck on You, the Farrellys seem to up the ante on tastelessness. Matt Damon and Greg Kinnear play Bob and Walt, conjoined twins. (Don't call them "Siamese," says Bob: "We're American.") The brothers are connected at the waist and share a liver—although Bob has most of it, which is unfortunate because Walt is the bigger drinker. The pair grew up on Martha's Vineyard, where they were stars on the sports teams. Flashbacks show them making a heck of a giant goalie; and, as a baseball pitcher, one could pretend to throw to the plate while the other picked off a runner—and what ump would dare to call a balk?

As grown-ups, Bob and Walt run the Quickie Burger eatery, where they turn burger-making into a wondrous ballet: Watch them chop, flip, squirt, top, and plate with dizzying precision. The problem is that Kinnear's Walt (who's the slicker one—he sleeps with all the girls, while Bob sits beside the curtained bed with headphones and a laptop) wants to go to Hollywood to be an actor. Bob, who has no choice but to go with him, gets massive panic attacks when his brother performs.

In L.A., the twins pester celebrities like Meryl Streep (Meryl Streep) and Cher (Cher), the latter of whom is trying desperately to spring herself from a dopey forensic detective series called Honey and the Beaze. Contractually free to pick her leading man, she opts for Walt, sensibly convinced that the studio would not agree to a romantic hero with an entire other person physiologically attached. They studio aquiesces, though, instructing the director, Griffin Dunne (Griffin Dunne), to keep Bob out of the frame. These are some of the movie's funniest scenes: Bob trying to make himself invisible (hyperventilating into a paper bag) while Walt acts opposite Cher, then Walt trying to be inconspicuous while Bob goes on dates with a cyber sweetheart who has no idea that he's conjoined.

Despite the farcical situations, the film is lower on gross-out set pieces than the brothers' other films. At times, it's downright muted. Damon gives an affecting—a serious—performance: His Bob is brainy, introverted, and hopelessly overdependent on his brother's initiative. And this is the first time I've warmed to Kinnear: He's very sweet, and his usual smarminess merges with the character's overconfidence in a way that's rather poignant. Stuck on You has patches of uncomfortable intimacy—moments when you realize that, for the Farrellys, this is personal. Near the end, the twins get into a fight and begin to slap each other, and when Bob sprints in the opposite direction Walt yells, "You'd better run!" That line is hilarious, but the blows that follow aren't accompanied by Three Stooges boinks. They're real. Then the brothers lie exhausted on the grass and wonder out loud if it's finally time to go under the knife.

When the Bijani twins of Iran died tragically this summer during surgery to separate them, there was clucking in some circles that the decision to release a conjoined-twins comedy was monstrous. But Stuck on You turns out to be an offbeat memorial to the Bijani's dilemma; and, beyond that, a metaphor for all our cruel intimacies. It's about how symbiosis makes you stronger, and warps you, while separation makes you liberated, and incomplete. The movie is a testament to compromise, and so are the Farrellys' other movies—between the freakish pain of living and the wonderfully dumb gross-out slapstick that said freakishness makes possible.

Tim Burton, on the other hand, hasn't so much compromised as neutered his anarchic instincts. Fifteen years ago, after the exhilarating Beetlejuice (1988), he boasted of subverting "the Spielberg story structure," and he cultivated his image as a cackling, inarticulate bad boy—the phantom of the Warners lot. It's a fair question whether Burton was being subversive or self-serving: My hunch is that he knew he had no gift for narrative and simply couldn't be bothered to deal with the connective tissue between set pieces. He liked flouting studio rules, and he liked adding a touch of Ed Wood Jr. tackiness to his big-budget movies. (He'd romanticized Wood's soulful ineptitude long before his 1994 biopic was a gleam in his eyes.)