What if Billie Holiday sang the modern poet-singer greats like Bob Dylan, Leonard Cohen, Joni Mitchell, Serge Gainsbourg, Tom Waits? That would seem unlikely, given that she died in 1959. But here's the next best thing: Madeleine Peyroux.
Her singing style is clearly inspired by Holiday, but her song selection is quite contemporary. Her blues tunes have a stronger, more rock-like beat than you'd hear from Holiday, while her jazzier selections (and contemporary singer-poet covers) have a nice swing to them. Her interpretations are original and fascinating. No casual pop singer she.
I just picked up her 2004 album "Careless Love", but her website contains complete streaming versions of all her albums (flash 8 required). Check her out.