Supergravity theories are better behaved in the ultraviolet than had been believed possible. It may even be true that certain theories supergravity theories, such as N=8 supergravity, are ultraviolet finite to all loop orders. We describe a new set of ultraviolet cancellations beyond those identified via standard symmetry arguments. We give examples in N=4 supergravity at three loops and N=5 supergravity at four loops.