The threshold collision-induced dissociation method is applied to study the fragmentation patterns and to measure the dissociation energies of small anionic copper clusters (Cu-n(-), n = 2-8) and their monocarbonyls (CunCO-, n = 3-7). For the bare clusters, the main reaction channels are loss of an atom and loss of a dimer. For the copper cluster monocarbonyls, the main channel is loss of CO. Dissociation energies for the loss of an atom from bare copper cluster anions, D-0(Cu-n-1(-)-Cu), show even-odd alternation. The species with the highest dissociation energy, Cu-7(-), and the highest carbonyl desorption energy, Cu5CO-, have eight valence electrons, consistent with closed shells in the jellium model. Bond energies are compared with theoretical models.