We consider the consequences for the relic neutrino abundance if extra neutrino interactions are allowed, e.g., the coupling of neutrinos to a light (compared to m(nu)) boson. For a wide range of couplings not excluded by other considerations, the relic neutrinos would annihilate to bosons at late times and thus make a negligible contribution to the matter density today. This mechanism evades the neutrino mass limits arising from large scale structure.