We consider a class of late-decaying dark-matter models, in which a dark matter particle decays to a heavy stable daughter of approximately the same mass, together with one or more relativistic particles which carry away only a small fraction of the parent rest mass. Such decays can affect galactic halo structure and evolution, and have been invoked as a remedy to some of the small-scale structure-formation problems of cold dark matter. There are existing stringent limits on the dark matter lifetime if the decays produce photons. By considering examples in which the relativistic decay products instead consist of neutrinos or electron-position pairs, we derive stringent limits on these scenarios for a wide range of dark matter masses. We thus eliminate a sizable portion of the parameter space for these late-decay models if the dominant decay channel involves Standard Model final states.PACS numbers: 95.35.+d, 95.85.Pw, 98.62.Gq, 98.70.Vc