  We study the role of perturbative unitarity in the resonant annihilation of
two dark matter particles into the standard model bath. Systematically
including all kinematically allowed holomorphic cuts of the corresponding
forward-scattering diagram, cancelation of the singularities occurs, resulting
in a fixed-order correction to the narrow-width approximation for the
annihilation cross section. Unlike the standard approach based on including the
finite width of the mediator, no double counting of intermediate states occurs.
