The exact nature of the hole traps reported deep in the band gap of Cu2O has been a topic of vigorous debate, with coppervacancies and oxygen interstitials both having been proposed as the relevant defects. In this article, the electronic structure of acceptor-forming defects in Cu2O, namely, coppervacancies and oxygen interstitials, is investigated using generalized gradient approximation (GGA) and GGA corrected for on-site Coulombic interactions (GGA+U). GGA produces notionally semimetallic defect complexes, which is not consistent with the experimentally known polaronic nature of conduction in Cu2O. GGA+U also predicts a semimetallic defect complex for the “simple” coppervacancy but predicts the “split” vacancy and both oxygen interstitials are characterized by localized polarons, with distinct single particle levels found in the band gap. For both methods, however, the positions of calculated transition levels are inconsistent with experimental ionization levels. Hence neither GGA nor GGA+U are successful in modeling p-type defects in Cu2O.