I have a Jamis Aurora. It came with 700x32 Vittoria Randonneur tires. I'm wondering if I can switch to 28c and still use the same rims? Reasons are,

1. I need a new tire and I can't find any 32's in stock anywhere, and
2. I figure 28's might be a little faster anyway...

I want to stick with the same tires unless I can't find what I want. I've only had one flat in two years, riding through all kinds of l.a. road debris, that wasn't caused by user error and the ride seems pretty grippy to me.