Since everyone was doing it, why not make another cover to "Little Bitty Pretty One"? That's exactly what The Jackson Five did to open up the B side of their album Lookin' Through The Windows.
Originally Bobby Day and The Satellites recorded the song in 1957(which you can listen to Here). Followed by Thurston Harris. Every decade ever since has featured at least a remake. Even as late as 2000!
Personally, I like every version. Of course, The Jackson Five infuse a little Soul into the mix.