We explore a dark-matter model in which there are two dark-matter species nearly degenerate in mass, with epsilon = Delta M/M << 1. The heavier particle undergoes two-body decay with a half-life tau, to the lighter dark-matter particle and a noninteracting massless particle. Unlike previous work on decaying dark matter, we explore the regime tau > 100 Myr and non-relativistic kick speeds vk / c = epsilon. Using a set of N-body simulations of isolated dark-matter halos, we show how halos change as a function of tau and vk. We find that tau < 40 Gyr is ruled out for vk > 20 km s^{-1} (epsilon > 10^{-4}) when we compare the simulations to observations of dwarf-galaxy- to cluster-mass dark matter halos. We highlight which set of observations should provide better future constraints for decays and other types of dark-matter physics.