Musicals are so off-putting to some that it’s likely even the ­blackest-souled fans of Tim Burton and Johnny Depp might hesitate before buying a ticket to their latest collaboration, Sweeney Todd: The Demon Barber of Fleet Street. How many throat-slittings would provide adequate compensation for sitting through a nearly two-hour film driven by Stephen Sondheim songs? The pairing of the murder-and-meat-pies Broadway hit and Hollywood’s go-to Goths seems natural, but a few picky pallids may find cannibalism a bit distasteful when accompanied by a tune.

Unfortunately, more than the score sinks Sweeney Todd. It’s not a bad film—grading on a curve, it’s actually rather enjoyable. Burton-Depp devotees salivating for a bleak holiday blockbuster need to dial down their expectations, though. Screenwriter John Logan pared down the Sondheim-Hugh Wheeler stage version but hewed closely to the story: It’s 19th-century London, and Benjamin Barker (Depp) has just returned from Australia, where he was imprisoned for 15 years by a judge named Turpin (the always terrifically oily Alan Rickman), who was in love with Barker’s wife. Barker, now calling himself Sweeney Todd, discovers that his wife killed herself, but his daughter, Johanna (Jayne Wisener), has been living as a virtual prisoner of Turpin’s. Todd wants revenge, but first he sets up a barber shop above a desolate meat-pie store run by a bad cook named Mrs. Lovett (Helena Bonham Carter).

Todd’s first homicide was unplanned, provoked by a customer who saw past the bride-of-Frankenstein hair and recognized the barber as Benjamin. But what Todd and Lovett lack in melanin, they make up for in brains: Murder is really just a bad shave waiting to happen, and meat prices being what they are, grinding the fresh corpses into pies might just save Lovett money and face. (Carter’s introductory song, “The Worst Pies in London,” is one of the production’s best, uptempo and funny.) It’d only be a matter of time before Todd has Turpin in his chair. Meanwhile, Todd encourages a young sailor (Jamie Campbell Bower) with eyes for Johanna to help rescue her.

Sweeney Todd’s cinematography has a fitting shades-of-gray palette that evokes poverty, oppression, and death. The opening is particularly Burton-esque, with a swirling, urgent, cartoonish string score accompanying images of meat grinders and blood so acrylic-red it could be leftover candy from the Charlie and the Chocolate Factory set. The bizarro-world kid-friendliness doesn’t last, of course—there are quite graphic, torturously slow throat-slicings and, well, the singing. None of the majors have terrible voices, but many of Sondheim’s tunes aren’t very memorable, which makes several segments of the film drag. (Edward Sanders, however, as a boy who helps around the shop, slays his co-stars whenever he uses his Broadway-ready pipes.)

Worse, Depp seems confined. He glowers and offs his clientele with verve, but otherwise he doesn’t bring much notable to the character. (Exceptions: His eye-rolling reactions during “By the Sea,” Lovett’s pondering of a potential romantic relationship, are amusing, as is the anomalous Crayola-colored picnic scene as a whole.) Carter and Rickman are similarly solid but unspectacular; the most entertaining performance by far is Sacha Baron Cohen’s brief appearance as an outrageously dressed and accented Italian con man. Of all the musicals in all the world, Sweeney Todd was undoubtedly the perfect choice for this filmmaking team. But fans of both the stage version and the Burton crew may find the adaptation too by-the-numbers to really slay ’em.