This is one of those songs that has a interesting tangle of derivative versions. It may even be some kind of parallel creativity happening simultaneously in different place (but I doubt it).
My understanding is that Littlefield released his version of the blues song 'K.C. Loving' in 1952, and that Harrison often performed a cover of this tune.
Now I don't know the timing of this, but either in late '58 or early '59, Wilbert Harrison cut his calypso-esque, bluesey-rocking version with a trio in a N.Y. recording session. Either just before or just after this recording session, Leiber and Stoller "wrote" the song too (1959). I don't know whose version Harrison sang on that record: Leiber and Stoller were brilliant and prolific writers with a great deal of music-business savy, and theirs are the names legally affixed to the song. I have too much respect for Leiber and Stoller's many finger-snapping accomplishments to accuse them of ripping off a black singer, but I wish I could ask Wilbert Harrison what he thinks went down. In any case, it's all part of the derivative flow of singing and song writing.

Mark