Recent numerical studies(1-5) suggest that ＇rubble-pile＇ asteroids (gravitationally bound aggregates of collisional debris) are common in the Solar System, and that self-gravitation may equal or exceed material cohesion for planetary bodies as small as several hundred metres. Because analytical scaling relations for impact cratering and disruption(6-8) do not extend to this size regime, where gravity and material strength are both important, detailed simulations are needed to predict how small asteroids evolve through impact, and also to ascertain whether powerful explosions offer a viable defence against bodies headed for a collision with Earth. Here we present simulations, using a smooth-particle hydrodynamics code(9), of energetic impacts into small planetary bodies with internal structure ranging from solid rock to porous aggregate. We find that the outcome of a collision is very sensitive to the configuration of pre-existing fractures and voids in the target. A porous asteroid (or one with deep regolith) damps the propagation of the shock wave from the impactor, sheltering the most distant regions, while greatly enhancing the local deposition of energy. Multiple-component asteroids (such as contact binaries) are also protected, because the shock wave cannot traverse the discontinuity between the components. We conclude that the first impact to significantly fragment an asteroid may determine its subsequent collisional evolution, and that internal structure will greatly influence attempts to disrupt or deflect an asteroid or comet headed towards Earth.