Few actors take reckless deep-end lulus like Johnny Depp. So it’s no surprise that, from the start of Sweeney Todd: The Demon Barber of Fleet Street, Depp is utterly convincing in the title role of a prosperous London barber turned into a shell-socked soul who’s stared at the face of human evil and is eager to slice its gullet.

Sure, Depp can do crazy and Cockney; his all-purpose Jack Sparrow accent turns up again. But how can someone who likened his singing to a strangled cat ever make it through the winding counterpoint style of Stephen Sondheim’s opuses?

Some of what Tim Burton shaves from Sondheim’s story for his campy, but respectful, take leaves visible nicks, but his film is perfect in one respect: Johnny Depp really can do everything. His singing is a pleasurable revelation — a David Bowie-esque husk with boiled-over punk-rock emotion, Roger Waters’ shouting rage and all the psychotic Sondheim showmanship necessary.

Wrongfully imprisoned by Judge Turpin (Alan Rickman), a lecher who coveted his lovely wife, Sweeney returns to London with revenge on his mind. After learning of his wife’s death and daughter’s imprisonment as the vile judge’s intended child bride, Sweeney re-opens his shop. It now sits above the city’s worst meat-pie shop, operated by Mrs. Lovett. Despite her garbled diction in song, Helena Bonham Carter offers a jovial, corpse-complexion complement to Depp’s intensity.

Sweeney’s singular drive for revenge turns into consuming homicidal rage after a threat of blackmail from rival barber Pirelli. Sacha Baron Cohen plays Pirelli as a cross between Napoleon and a matador who leads with an amusingly, artificially stuffed crotch and sings like Billy Crystal’s Fernando. And Mrs. Lovett makes her own pie-making play to benefit from all of Sweeney’s slicing.

Thanks to a hefty cinematic score and expert editing by Chris Lebenzon, Burton keeps the music, and movie, moving. At a quick two hours, it nevertheless suffers from two song omissions.

Without “Kiss Me,” the “love story” between young sailor Anthony (Jamie Campbell Bower) and Sweeney’s daughter Johanna (Jayne Wisener) dissipates into nothingness. (As if no one ever had gazed up at the pubescent beauty’s window from the street before.) And what a waste to hear Rickman sing Judge Turpin’s version of “Johanna” only as a snippet during “Pretty Women” rather than flogging himself in self-loathing during the full arrangement riddled with sexual angst.

Still, Burton expands horizons into larger London — and, in a hilarious dream sequence, a seaside getaway — while never losing live-stage intimacy. It’s filled with Burton’s hallmarks of off-kilter stylization and bleak humor, but he captures the devastating complexities of this sinister tale.

When the blood starts to spurt, sputter and spit, it’s in just the right shade — not so thick and crimson as to be off-putting but not so fake and thin as to have no impact. In the Italian-horror vein, it’s comically overwrought and gratuitously gross at once, even splattering the camera. Burton remembers, though, to use it as ink for the final stanzas of this entertaining piece of graphic poetry.