We compute the cross-sections for the radiative capture of non-relativistic particles into bound states, in unbroken perturbative non-Abelian theories. We find that the formation of bound states via emission of a gauge boson can be significant for a variety of dark matter models that feature non-Abelian long-range interactions, including multi-TeV scale WIMPs, dark matter co-annihilating with coloured partners and hidden-sector models. Our results disagree with previous computations, on the relative sign of the Abelian and non-Abelian contributions. In particular, in the case of capture of a particle-antiparticle pair into its tightest bound state, we find that these contributions add up, rather than partially canceling each other. We apply our results to dark matter co-annihilating with particles transforming in the (anti)fundamental of SU(3)c, as is the case in degenerate stop-neutralino scenarios in the MSSM. We show that the radiative formation and decay of particle-antiparticle bound states can deplete the dark matter density by (40-240)%, for dark matter heavier than 500 GeV. This implies a larger mass difference between the co-annihilating particles, and allows for the dark matter to be as heavy as 3.3 TeV.