So, I stumbled on a new (to me) girl for this thread just a few minutes ago. Unfortunately, I can't find a YouTube of her singing the song that turned me on to her. Anyway, the woman's name is Rickie Lee Jones, and her song "Trouble Man" is absolutely hot. Unfortunately, the only link to it I have is a 30 sec preview clip from emusic.com, but it's the best I can do:
Trouble Man
She has a neat cover of Steely Dan's Show Biz Kids on that same album.
I didn't dig the other stuff of hers quite as much, but
Chuck E's In Love was pretty interesting, too.