All I want for Christmas is a new album by Dee Alexander. Alas, she's still working on her debut studio disc, but for anyone who's heard her onstage lately--or heard her contributions to recent albums by local trumpeters Orbert Davis and Malachi Thompson--even the promise of one is enough to trump everything else on the wish list. A true jazz diva in the mold of Sarah Vaughan, Dinah Washington, and Dianne Reeves, Alexander has an innate theatricality and enough pure musicality to overwhelm most of the instrumentalists with whom she shares the stage. She swings without effort, and rhythmically she's so assured that she can take extensive detours around the beat without losing the audience. She applies that same authoritative ease to intonation: she can hit any note she chooses, which makes her husky alto a potent weapon whether she's singing a stomp or a ballad. Yet for all that, she's strongest as an improviser, especially when she mimics a horn: Alexander does a drop-dead imitation of trumpet and trombone, down to the idiosyncratic growls and smears of both, and she can trade solos with any wind player willing to engage her. In those moments, when she drops even the pretense of verbal language offered by scat syllables, she enters a realm of pure musical thought that most singers only dream about. She'll be joined by pianist Miguel de la Cerna, bassist Harrison Bankhead, and drummer Leon Joyce. See also Saturday. Fri 12/2, 9 PM, Green Mill, 4802 N. Broadway, 773-878-5552, $10.