My family and I are heading to RAGBRAI this summer, and I'd like to put some skinnier, higher pressure slicks on my wheels for RAGBRAI. (We're currently stuck with 26x2.0 tires because our house requires us to ride 1.5 miles each way over nasty, loose gravel to get to paved roads to ride.)

I've seen a few 100psi 32mm and 35mm tires I'd like to try, but I'm not sure how narrow I can go and still have the tire adequately support the weight of the bike. What is a safe width for tires that need to support 250+lbs each? (If it matters, the wheels are 26" w/36h hubs.)