  We consider a class of models of neutrino mixing with $S_4$ flavour symmetry
and generalised CP symmetry, broken to $Z_2$ and $Z_2 \times {\rm CP}$ residual
symmetries in the charged lepton and neutrino sectors, respectively. In this
scheme, and up to discrete ambiguities, the neutrino mixing matrix is
determined by two angles and one phase. We classify the phenomenologically
viable mixing patterns, deriving predictions for the Dirac and Majorana CPV
phases and for the effective Majorana mass in neutrinoless double beta decay.
