Not every flat results in a bead break. A length of 1" nylon strap takes up little room, and can be used to reposition the bead enough to inject air (or CO2) to pop it in place. This works better with the Schraeder valve removed. If you're at a loss as to how to tighten the strap, grip the strap ends with needlenose pliers and roll the pliers. I've seen a tool similar to a strap wrench that grips the strap and is tightened with a ratchet, but I've no idea where to get one.