A ball dropped over a solid surface bounces several times before a complete stop. The bouncing can be reduced by introducing a liquid into the ball; however, the first rebound remains largely unaffected by the fluid. Granular materials can also work as dampers. We investigated the rebound of a container partially filled with a given mass of grains mi. During the collision, the kinetic energy of the container is partially transferred to the grains, the rebound is damped, and the fast energy dissipation through inter-particle collisions and friction decreases the bouncing time dramatically. For grain-filled cylinders, a completely inelastic collision (zero rebound) is obtained when mi ≥ 1.5εomc, where εo and mc are the coefficient of restitution and mass of the empty container. For grain-filled spheres, the first rebound is almost undamped, but the second collision is completely inelastic if mi ≫ mc. These findings are potentially useful to design new granular damping systems.