I just ran across this great version of the song. I didn't know it was written by Jerry Lieber and --not in this case Mike Stoller, but -- Artie Butler. A beautiful bit of singing by New Orleans R&B singer Alvin Robinson: http://funky16corners.lunarpages.net/?p=1755.
Then check out the quite different Coasters' version. The Stones version: http://www.youtube.com/watch?v=Fp2q3yK8Lrs
Apparently there are no CDs or compilations of Alvin's singing -- a shame. Lost in time.