hats

Is it possible to get a tight enough hat band using a three and one ribbing - ie knitting three stitches and purling 1? I'm trying to figure out if I
a. have too many stitches
b. need smaller needles or
c. need to give up on the idea of a 3-1 ribbing since it won't ever be tight enough.

I actually undid three hours of knitting because the hat was on track to be too loose. As much as it troubled me to frog, I knew it would bother me every time I wore the hat - if I ever wore it - if I didn't. Besides, the fair aisle I was trying out wasn't showing up as much as I would have liked anyway.

Maybe I should swatch? Now that's just a radical thought!