Smallest tire on 15" rim?

Im hopefully purchasing my first tube chassis car next weekend and as much as I like the 33/16's on the back of this thing I would like to run a smaller tire,(drag radial),on the street and was wondering what the smallest tire is that I can fit on a 15" wide rim. I think I may have to got to a 12" rim to get the look I want but I also dont want to give the car so much of an "overbite" look. Any suggestions?