I'll Resurrect this thread. You want little known tunes? You want 80s little known tunes?
Kajagoogoo - click at your own risk
Men at Work are very popular, but this song doesn't get the play as some of their more famous hits.
And who doesn't like Weird Al? This work of his is my favorite and I'm pretty sure its not terribly well-known compared to some of his other stuff. lol