  We show that it is possible to implement soft superweak CP violation in the
context of a 331 model with only three triplets. All CP violation effects come
from the exchange of singly and doubly charged scalars. We consider the
implication of this mechanism in the quark and lepton sectors. In particular it
is shown that in this model, as in most of those which incorporate the scalar
mediated CP violation, it is possible to have large electric dipole moments for
the muon and the tau lepton while keeping small those of the electron and the
neutron. The CKM mixing matrix is real up to the two loop level.
