  The minimal 3-3-1 model is perturbative until energies around 4-5TeV, posing
a challenge to generate neutrino masses at eV scale, mainly if one aims to take
advantage of the seesaw mechanism. As a means to circumvent this problem we
propose a modification of the model such that it accommodates the type I and
type II seesaw mechanisms altogether. We show that the conjunction of both
mechanisms yield a neutrino mass expression suppressed by a high power of the
cutoff scale, $M^5$, in its denominator. With such a suppression term we
naturally obtain neutrino masses at eV scale when $M$ is around few TeV. We
also investigate the size of lepton flavor violation through the process $\mu
\rightarrow e\gamma$.
