IT'S NOT JUST the child actors who look all grown up in "Harry Potter and the Prisoner of Azkaban." The filmmaking does, too. "Azkaban," the third installment in the Harry Potter series, is everything the first two films were not: complex, frightening, nuanced. The Potter purists who were so sorely affronted by the choice of Chris Columbus to direct the first two films expected great things from Alfonso Cuaron -- director of the Oscar-nominated "A Little Princess" and "Y Tu Mama Tambien" -- and they are not likely to be disappointed. "Azkaban" is so much more sophisticated visually, and in terms of storytelling, that it's hard to believe the source material is the same. It's not perfect, or even close, but it delivers on the promise of J.K. Rowling's novels to a far greater extent.

Before the series is done, it will offer audiences something of a cinematic education -- at least in terms of directorial style. Consider, for example, that Columbus, of "Home Alone" fame, directed the first two Harry Potter movies and that Mike Newell ("Four Weddings and a Funeral") will direct the fourth, which starts shooting next month. Throw in Cuaron and whomever else it takes to complete all seven projected films, and you've got the same material filtered through multiple sensibilities -- some of which, we can now say with confidence, are much better suited to it than others.

Directorial interpretation aside, it's entirely fitting that the more grown-up book gets the more grown-up movie. "Harry Potter and the Prisoner of Azkaban" is the best of the five Harry Potter novels, and it's markedly different from the two that precede it. With its ominous mood and surprise ending, it's less like a fairy tale and more like a whodunit. (Not that there's any reason for these movies to be sunny. At their most fundamental level, the series is about coping with the death of a parent -- something which, finally, comes across here. Only in a work of fiction could it invariably be considered such a precious compliment for people to say they see your parents in you.) Cuaron's wholesale disavowal of cuddliness couldn't have come at a better time.

At the start of his third year at Hogwarts School of Witchcraft and Wizardry, Harry learns that Sirius Black, the wizard whose betrayal of his parents resulted in their deaths, has escaped from Azkaban, the wizarding equivalent of a maximum-security penitentiary -- and he's coming after Harry. The film opens with our hero finishing out the summer holidays at the home of his Muggle -- non-wizarding -- relatives. It's clear from the outset that this is Harry with an edge: When he is insulted beyond endurance by the loathsome Aunt Marge and the dishes begin to rattle and shake, it's hard to miss the "Carrie" reference. Like the film as a whole, Harry's human family is less cartoonish here, and therefore more threatening- less cartoonish, that is, except for the part where Harry's Aunt Marge inflates like a middle-aged Violet Beauregarde and floats away.

This Harry no longer inhabits a primary-colored world. In Cuaron's film, which has a palette of dull browns and grays, it's almost always dark, wet or both. The locations have undergone a similar transformation. The Leaky Cauldron, for one, is no longer a Magic Kingdom-style tavern, but a dirty and sinister place, one where you'd do well to keep an eye on your wallet. Not even Hogwarts seems quite so inviting. The building is now Gothic rather than baroque, and the director has picked it up and set it down in a desolate mountainous landscape. The school's dress code seems to have been relaxed as well. Robes and witches' hats are still in evidence, but the kids spend most of their time in street clothes. Even bus conductor Stan Shunpike's pimples and greasy hair seem designed to strike a new note of (relative) realism.

Aside from the radical change of mood, the biggest difference in "Azkaban" is the burgeoning maturity of the film's three lead actors. Harry (Daniel Radcliffe), Hermione (Emma Watson) and Ron (Rupert Grint) look older, old enough for there to be -- ewww -- sexual tension between Ron and Hermione. (It seems altogether appropriate when, at one point, Harry uses his invisibility cloak like a fake ID, entering a bar where underage wizards aren't allowed.) Like its predecessors, the film includes cameos by a slew of fine British actors, some of whom make something of their fleeting screen time (Alan Rickman's Professor Snape is still a formidable presence) and some of whom don't (Emma Thompson's goofy turn as Professor Trelawney would have been a much better fit in one of the Columbus movies). The real surprise in this category is David Thewlis as Professor Lupin, who inexplicably eschews his customary air of menace in a role that require just that. It may be that working with the likes of Kenneth Branagh and Maggie Smith has had some long-term benefits for the young actors: All three give more subtle performances than before -- even Grint keeps his mugging to a minimum this time around.

The best thing about "Azkaban" is its success at capturing and elaborating on the details that make the books such a delight. The Whomping Willow, always dangerous, is now apparently carnivorous; passing birds disappear into its foliage and their feathers drift gently to the ground. Cuaron hangs familiar Old Masters among the living paintings in the school's stairwell; at one point, an angry Rembrandt self-portrait shushes Harry. Rowling's book introduced the hippogriff -- half griffin, half horse -- but it's Cuaron who answers the question, "What do hippogriff droppings look like?" During one classroom scene, Professor Lupin puts on a jaunty phonograph record, giving a harrowing magic lesson a disconcerting choreographed effect.

Because of its position in the lineup, "Harry Potter and the Prisoner of Azkaban" suffers from what you might call Low Bar Syndrome. It's so easy to quantify the ways in which it's better that you lose sight of whether it's good. Certainly the film is not without its disappointments: The Dementors, spectral Azkaban prison guards and Rowling's metaphors for depression, look an awful lot like crepe-draped basketballs. The pacing is slightly off kilter: some sequences pass in a flash, while others seem to unfold in real time. And the plot -- although the film is better for not being overloaded with exposition -- can be hard for the uninitiated to follow. (Good news for those of us who've wondered when being the kind of nerd who's read the books again and again will pay off.)

Still, such imperfections seem a small price to pay for a Potter film with fangs.

HARRY POTTER AND THE PRISONER OF AZKABAN (PG, 142 minutes) -- Contains fisticuffs, an implied beheading and a sad sack werewolf. Area theaters.

Steps in the right direction: Emma Watson, Daniel Radcliffe and Rupert Grint, from top, go deeper into the spirit of the books in "Harry Potter and the Prisoner of Azkaban."