When it was announced about a year ago that Scarlett Johansson was recording an album of Tom Waits songs, many commentators feigned a kind of exasperated surprise, as if the idea of an actress (or actor) taking a chance on a musical project was unknown. It’s not. Just ask Bruce Willis. Or Lauren Bacall, Marilyn Monroe, Clint Eastwood, Raquel Welch, Cybill Shepherd, Diane Keaton, Sissy Spacek, Rex Harrison, Kevin Bacon, Robert Downey Jr., Jeff Bridges, Lee Marvin, John Travolta, Jack Nicholson, Burt Reynolds or Robert Mitchum. Nor is the reverse career path so unusual, as Frank Sinatra, Bing Crosby, Bowie, Elvis, Prince, Madonna and J-Lo have established.

But the Johansson project was unusual from the start. The Sexiest Woman Alive (2006 version) takes on the Rain Dog. Obviously something more than the usual pop record. But once you get past the sheer delight of that juxtaposition, more practical doubts arise. Can she sing? Is this some kind of a joke, like Shatner recording songs by Pulp?

Johansson’s album, “Anywhere I Hang My Head” (due in stores May 20), proves to be harder to pin down that you might have expected. It’s not disposable celebrity pop (you’d hardly go with an all-Waits lineup if that was the plan), nor is it sheer self-indulgence along the lines of “The Return of Bruno.” Under the production of “TV on the Radio’s” Dave Sitek, the album recalls the various tribute albums to Monk, Weill, Mingus and others produced by Hal Willner. The idea seems to be a flowing collage of Waits’ songs in which the vocals aren’t the main attraction – the album even starts with an instrumental, “Fawn,” from Waits’ “Alice” – but just one aspect among many sonic textures. (They even come close to being buried by the arrangements on some songs, like the strange techno-pop revision of “I Don’t Want to Grow Up.”)

But how is the singing? How does Johansson’s voice compare with Waits’ own ragged but undeniably expressive whisky-soaked tone? I’ll admit that I was slightly surprised by her take on these songs, which has neither the raspy growl of the originals nor the trained-but-slumming approach of earlier interpreters like Ute Lemper. Her register is lower than I expected, and she tends to favor a dry, almost emotionless delivery that recalls early-’80s new wave/pop, but this too may be a deliberate choice on the part of Sitek to make the vocals fight for attention over the musical arrangements.

And is it good? Well, it’s certainly listenable, though most hard-core Waits fans won’t hesitate in turning back to their copies of “Bone Machine” and “Frank’s Wild Years.” If it introduces a new audience to Waits, so much the better. If it encourages Johansson to keep stretching herself and make some equally daring follow-up, that’s fine, too. Me, I’m hoping it starts a trend. Anyone else up for “Reese Witherspoon sings Nick Drake”?