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We discuss two options of a scenario in which light neutrino masses are generated by the inverse seesaw mechanism (ISS) and the form of the coupling and mass matrices is determined by flavour and CP symmetries and their residuals. Results for lepton mixing and different signals of charged lepton flavour violation (cLFV) are presented. While for option 1 cLFV processes are highly suppressed, the studied parameter space of option 2 can be considerably constrained by the future limits on mu -> 3 e and mu-e conversion in aluminium.