The detonation properties of mechanically activated mixtures of ammonium perchlorate and aluminum were studied. The deflagration-to-detonation transition for low-density charges was investigated. Dependences of the detonation velocity of pressed charges with different types of aluminum on the activation time, density, and diameter of the charges were obtained. For compositions with nanosized aluminum, it is was found that the detonation velocity depends nonmonotonically on the inverse charge diameter and remains almost unchanged in a certain range of charge diameters. It is shown that the joint use of mechanical activation and nanosized components of the composite explosive significantly increases the detonability, reduces the critical diameter, and shifts the maximum of the detonation velocity as a function of density to higher charge densities.