But can she sing?

NO, really – Hollywood actress Scarlett Johansson shows off a lovely voice and leaves you wanting more with this debut

SCARLETT JOHANSSON: ANYWHERE I LAY MY HEAD ****

RHINO, £11.99

ACTORS, eh? Why won't they stay in their acting box and leave music to the musicians? Russell Crowe, Keanu Reeves, and even little Billy Boyd have all lost a bit of their screen shine with their pedestrian rock efforts, though some have crossed the divide with greater success. Commercially, at least, doe-eyed heartthrob Jared Leto now has a viable second career fronting dire emo rockers 30 Seconds To Mars, while it's easy to forget that J-Lo made her name as an actress before surpassing her thespian efforts in the pop realm. Juliette Lewis, meanwhile, has made a convincing stab of letting it all hang out with her garage punk band The Licks.

Out on the fringes, there have been a handful of intriguing alliances between the pop and film worlds. Jarvis Cocker, Neil Hannon and Air all wrote for Charlotte Gainsbourg's 5:55 album. More recently, Zooey Deschanel, who sang very prettily in The Assassination Of Jesse James By The Coward Robert Ford, hooked up with troubadour M Ward while filming The Go-Getter and the pair have recorded an album of 1960s-inspired material using the moniker She & Him.

But this is something different again – an A-list Hollywood actress laying her red carpet starpower to one side and losing herself in an album of Tom Waits covers. Anywhere I Lay My Head could have been a gross vanity project for Scarlett Johansson. She has been dismissive of her early efforts to bring her idea to fruition, but the pieces eventually came together when she fell in with hip New York producer Dave Sitek, a member of mercurial Brooklyn band TV on the Radio and the man behind the mixing desk on many buzz recordings of the past year. Thanks to his involvement, Johansson was able to call on the services of Yeah Yeah Yeahs' stellar guitarist Nick Zinner, and their mutual friend David Bowie for backing vocals on a couple of tracks.

Apparently a long-time Waits fan, she has selected tracks from some of his best loved albums – Swordfishtrombones, Bone Machine and the title track from Rain Dogs among others. On the sleeve photograph, which recalls Kylie as the Wild Rose to Nick Cave's murderous lover, she looks like a character from a Waits song. Yeah, but can she sing? It's all deliciously intriguing.

She makes you wait to find out – there is no audible sign of Johansson on opening track Fawn. I'd heard that her voice was low, but is it actually subsonic? Nope, this is just an atmospheric instrumental warm-up stamped with Waitsian organ and discordant brass squall, while Johansson ponders her motivation for her first scene, Town Without Cheer.

Three minutes into the album and she still hasn't opened her mouth. Some guy starts emoting beautifully and… okay, her voice really is that deep. It's a haughty, glacial tenor, intoning like Velvet Underground chanteuse Nico as she is consumed by the encroaching organ swirl and funereal horns. Intoxicating.

For the following song, Falling Down, she's on some astral country plane, channelling the voice of Cocteau Twins' Liz Fraser, while Sitek creates his very own Jesus & Mary Chain track, with added banjo and music box magic.

Of all the tracks on the album, Green Grass is the one which strays the least from Waitsworld – with its muted junkyard blues feel, it wouldn't sound out of place on the current Isobel Campbell/Mark Lanegan album – but elsewhere the emphasis is on reinterpreting Waits's songs.

Fannin' Street's hymnal melody is teamed with a Phil Spectorish backing, which may be where some of the comparisons with Ronnie Spector's voice have arisen. Johansson is really no ballsy soul heartbreaker but her voice is well served by Sitek's production choices. Although rarely the most prominent element in the mix, she does still provide an alluring focus around which Sitek's evocative arrangements dance.

The album boasts a generally cohesive sound but there are a couple of diversions, including the bubblegum indie synth pop of I Don't Want To Grow Up and the twinkling I Wish I Was In New Orleans, which evokes a breath of old Hollywood with a very pretty vocal which is practically falsetto by Johansson's standards.

And tucked right in the middle of the album there is one Johansson/Sitek original, called Song For Jo, which nestles comfortably enough in the company – if anything, it is actually more dirge-like than the Waits numbers, but has a softer, less dramatic edge. However, it's not a great song. If Johansson wants to pursue a singing career, maybe she could enlist the songwriting services of Stephin Merritt (The Magnetic Fields and others) for her next album? Or perhaps Mr Waits could oblige with some bespoke material? Because, unusually for an ATS (actress-turned-singer), Scarlett Johansson has made an album which leaves you wanting more.