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We perform an exhaustive theoretical study of the phase diagram of Cu–I binaries, focusing on Cu-poor compositions, relevant for p-type transparent conduction. We find that the interaction between neighboring Cu vacancies is the determining factor that stabilizes nonstoichiometric zincblende phases. This interaction leads to defect complexes where Cu vacancies align preferentially along the [100] crystallographic direction. It turns out that these defect complexes have an important influence on hole conductivity, as they lead to dispersive conducting p-states that extend up to around 0.8 eV above the Fermi level. We furthermore observe a characteristic peak in the density of electronic states, which could provide an experimental signature for this type of defect complexes.