The pinched tube usually happens in one of two places: either where the valve stem is, or at the place you last got the bead on the rim. Before doing ThermionicScott's process, first push the valve stem all the way in until it either bottoms out on the far side of the tire or you push it flush with the rim. Then let internal air pressure push it back out. That'll make sure the bead isn't sitting on the reinforced part of the tube.