This song dates back so far that it's hard to decide who wrote it. I think that the verse about the Mountain Jack that Steve-o is quoting is from "How long, how long blues" and has been inserted. Walter Davis recorded a "New Come Back Baby" around 1937, which is interesting - many sources credit this as the original, but the "New" in the title suggests new lyrics to an older tune. The Ray Charles version is credited to Mance Lipscomb: As far as I can see, so is the Stefan Grossman version. I have these lyrics from a forgotten source, which purport to be the Mance Lipscomb lyrics, but I don't have a recording to verify them.

COME BACK BABY

Come back, baby, Please don't go
The way I love you, baby you'll never know.
Come back, baby, let's talk it over one more
time.


My hearts in touble and in misery,
Ain't got nobody talk sweet talk to me,
Come back baby, let's talk it over one more time.


Hmmmmm, lonesome day,
Seem like tomorrow gonna be the same old way.
Come back baby, let's talk it over one more time.


Went up on the mountain, looked down at the sun,
Ain't seen nobody love me like you have done,
Come back baby, let's talk it over one more time.



Since Mance Lipscomb was not a Blues singer in the strict sense, I think it unlikely that he actually wrote the song.