Careless Love
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That's Elliot Smith's "Between the Bars", but it sounded like it was being sung by Billie Holiday.
I did a little research and found out it was a cover by Madeleine Peyroux on her CD Careless Love (here's another review).
I liked it, so I might check out her stuff if I remember. If you like Elliot Smith, you should try to hear that song.