Who are your three favorite female singers?

Jann Arden
Karen Bergquist (Over The Rhine)
Neko Case
Rosanne Cash
Dominique Durand (Ivy)
Martha Johnson (Martha & The Muffins)
Marti Jones
Wendy MaHarry
Michelle McAdorey (Crash Vegas)
Johnette Napolitano (Concrete Blonde)
Hope Nicholls (Fetchin Bones)
Sinead O'Connor
Sam Phillips
Kim Richey
Tracey Thorn (Everything But The Girl)

Also, check out Austin guitarist Monte Montgomery's cover of "Sara Smile" when he was a guest on Live At Daryl's House way back in the early days when it was just an internet only show. 

Norah Jones

Diana Krall

Emily King (you really need to listen to her)

Got to get in on this one. Joni and Natalie.  

Joan Osborne...

and then some others:

Bonnie Raitt
Nora Jones

Ofra Haza, sadly, died way too young. Her influence extended to all genres
Zehava Ben -https://www.youtube.com/watch?v=zkyorHkaJUA&list=FLo3s50L1lQEDx96RGgD0ZNQ&index=143
Rhiannon Giddens
Sooo many, very hard to limit to 3, as others observed; trying to limit it to 3 singers who are fantastic, belong in the top tier, but sadly unmentioned