Know any good songs I could sing?

A friend of mine asked me to sing some songs with their band. They usually focus on blues and rock but are looking to possibly switch it up. I need some ‘obscure’ suggestions we can use for covers – maybe some forgotten treasures, things that show off the singing more than the music because frankly, the guitarist is fail. We all came up with these possibilities to try out:

Julie London – Cry Me A River
Dusty Springfield – Son of a Preacher Man
Madeleine Peyroux – You’re Gonna Make Me Lonesome When You Go
Lena Horne – Stormy Weather
CCR – Proud Mary
Oh, and I Put A Spell On You

I should mention, we have access to a saxophone. :D

Obviously we’re gonna change a bit of it, except Preacher Man. We’re all big fans of huge big band numbers (but we’re not sold on that yet) we may be able to change up, we’re looking for music from the 30s-60s. We’re open to pretty much any genre that would have some solid vocal performances. Any other ideas?

EDIT: If we end up recording what we come up with, I’ll post. Happy krose? :)