The experimental photoelectron spectra of di- and triatomic copper oxide anions have been reported previously. We present an analysis of the experimental spectra of the Cu-, Cu2O-, and CuO2(-) anions using equation-of-motion coupled-cluster (EOM-CC) methods. The open-shell electronic structure of each molecule demands a unique combination of EOM-CC methods to achieve an accurate and balanced representation of the multiconfigurational anionic- and neutral-state manifolds. Analysis of the Dyson orbitals associated with photodetachment from CuO- reveals the strong non-Koop-mans character of the CuO states. For the lowest detachment energy, a good agreement between theoretical and experimental values is obtained with CCSD(T) (coupled-cluster with single and double excitations and perturbative account of triple excitations). The (T) correction is particularly important for Cu2O-. Use of a relativistic pseudopotential and matching basis set improves the quality of results in most cases. EOM-DIPCCSD analysis of the low-lying states of CuO2- reveals multiple singlet and triplet anionic states near the triplet ground state, adding an extra layer of complexity to the interpretation of the experimental CuO2- photoelectron spectrum.