  We consider non-universal 'minimal' Z' models, whose additional U(1) charge
is a non-anomalous linear combination of the weak hypercharge Y, the baryon
number B and the partial lepton numbers (L_e, L_mu, L_tau), with no exotic
fermions beyond three standard families with right-handed neutrinos. We show
that the observed pattern of neutrino masses and mixing can be fully reproduced
by a gauge-invariant renormalizable Lagrangian, and flavor-changing neutral
currents in the charged lepton sector are suppressed by a GIM mechanism. We
then discuss the phenomenology of some benchmark models. The electrophilic
B-3L_e model is significantly constrained by electroweak precision tests, but
still allows to fit the hint of an excess observed by CDF in dielectrons but
not in dimuons. The muonphilic B-3L_mu model is very mildly constrained by
electroweak precision tests, so that even the very early phase of the LHC can
explore significant areas of parameter space. We also discuss the hadrophobic
L_mu-L_tau model, which has recently attracted interest in connection with some
puzzling features of cosmic ray spectra.
