I've got a pair of Weinmann centerpulls with Weinmann levers on my bike. The levers have a quick-release built into them, which allows the pads to be set quite close to the rim. The only limiting factor in closeness would be if the rims were out of true a bit. With the quick-releases open, my 700x28 tires drop right out with room to spare. I haven't tried it with 700x32, but it looks like they might clear the brakes. Obviously there's a limit somewhere.