Lepton mixing parameters from discrete and CP symmetries

We consider a scenario with three Majorana neutrinos in which a discrete, finite flavour group G(f) is combined with a generalized CP transformation. We derive conditions for consistently defining such a setup. We show that in general lepton mixing angles and CP phases (Dirac as well as Majorana) only depend on one single parameter theta which can take values between 0 and pi, if the residual symmetries are G(e) subset of G(f) in the charged lepton and G(nu) = Z(2) x CP in the neutrino sector. We perform a comprehensive study for G(f) = S-4 and find five cases which are phenomenologically interesting. They naturally lead to a non-zero reactor mixing angle and all mixing parameters are strongly correlated. Some of the patterns predict maximal atmospheric mixing and maximal Dirac phase, while others predict trivial Dirac and Majorana phases.