  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 non-stoichiometric 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.
