  We report the most general classification of 3-3-1 models with $\beta
=\sqrt{3}$. We found several solutions where anomaly cancellation occurs among
fermions of different families. These solutions are particularly interesting as
they generate non-universal heavy neutral vector bosons. Non-universality in
the SM fermion charges under an additional gauge group generates Charged Lepton
Flavor Violation (CLFV) and Flavor Changing Neutral Currents~(FCNC); we discuss
under what conditions the new models can evade constraints coming from these
processes. In Addition, we also report LHC constraints.
