  We perform a systematic analysis of Standard Model extensions with an
additional anomaly-free gauge $U(1)$ symmetry, to generate tree-level Dirac
neutrino masses. An anomaly-free symmetry demands nontrivial conditions on the
charges of the unavoidable new states. An intensive scan was performed, looking
for solutions generating neutrino masses by the type-I and type-II tree-level
Dirac seesaw mechanism, via operators with dimension 5 and 6, that correspond
to active or dark symmetries. Special attention was paid to the cases featuring
no extra massless chiral fermions or multicomponent dark matter with
unconditional stability.
