"Cry me a river" was written by Arthur Hamilton for a movie called Pete Kelly's Blues to be sung by Ella Fitzgerald, but in the end the idea of featuring the song was dropped. This is why the first recorded version of the song comes from Julie London:
The song can be looked at as a Jazz-Standard, and it has been done in a variety of styles. We will start with Ella's rendering of it, then you can compare it with the vocal style of Etta James. Ray Charles is contributing a rather big-band-ish version.
So, here we go with Sam Cooke, whose way to do the song is near to giving it a somewhat optimistic air. As a remedy to the danger of developing a rather positive mood in connection with the composition, I strongly recommend to listen to the version done by The Swans.
Last not least. pianist Brad Mehldau w/t friends adds a piece of academic Jazz chamber music based upon Arthur Hamilton's composition: