  On fitting the type II seesaw mechanism into the type I seesaw mechanism, we
obtain a formula to the neutrino masses which get suppressed by high-scale
$M^3$ in its denominator. As a result, light neutrinos are naturally obtained
with new physics at TeV scale. As interesting consequence, the mechanism may be
directly probed at the LHC by directly producing the TeV states intrinsic of
the mechanism. We show that the 3-3-1 model with right-handed neutrinos
realizes naturally such seesaw mechanism.
