Diana Krall THE GIRL IN THE OTHER ROOM (VERVE)

Crossover jazz superstar Krall here steps out for the first time as a songwriter, and that’s due in no small part to her becoming Mrs. Elvis Costello. She sings Elvis’s "Almost Blue" (a jazz-standard-in-the-making if ever there was one), and she wrote another six out of these 12 tracks with him. The credits are careful to delineate who did what lyrics and music, but fans will hear Elvis’s clear stamp in both, whether it’s the distinctive Costello-like rising figure in the opening verse of the melody on "Departure Bay" or the internal rhyme of "I have the skill/Still to disguise my tears" on "Abandoned Masquerade." Krall even shows off a trace of Costello-like vibrato on "Almost Blue."

The title track is the most provocative collaboration — when Krall sings a word like "threadbare" or a phrase like "the paper is peeling," she brings her voice down to a raspy, care-worn hush. But otherwise, their lugubrious ballad-tempo tunes meander along hooklessly. Krall does better with Mose Allison’s "Stop This World" (the album opener) and the Chris Smither blues "Love Me like a Man" (an early staple for Bonnie Raitt) or even Joni Mitchell’s "Black Crow" because she gets to swing as both pianist and vocalist and show off the hard-edged playing of her guitarist, Anthony Wilson. In fact, she’s best served here not by Costello but by Tom Waits, whose "Temptation" she delivers as a slow rumba, with bassist Christian McBride laying down melody and rhythm, a tambourine gently popping the last beat of every other measure, Neil Larsen playing spooky Waits-like Hammond B-3, and her own voice bending and swooping.

(Diana Krall performs this Tuesday, June 22, at FleetBoston Pavilion, 290 Northern Avenue in Boston; call 617-728-1600.)