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We consider a class of models of neutrino mixing with $S_4$ flavour symmetryand generalised CP symmetry, broken to $Z_2$ and $Z_2 \times {\rm CP}$ residualsymmetries in the charged lepton and neutrino sectors, respectively. In thisscheme, and up to discrete ambiguities, the neutrino mixing matrix isdetermined by two angles and one phase. We classify the phenomenologicallyviable mixing patterns, deriving predictions for the Dirac and Majorana CPVphases and for the effective Majorana mass in neutrinoless double beta decay.

Neutrino Mixing and Leptonic CP Violation from $S_4$ and Generalised CP Symmetries