  We show that the minimal 3-3-1 model cannot accommodate the neutrino masses
at tree level using present experimental data. Nevertheless, a modified Zee and
the Zee-Babu mechanisms for generating neutrino masses at 1-loop and 2-loop,
respectively, are automatically implemented in the minimal 3-3-1 model, without
introducing new degrees of freedom to the model. We also present a systematic
method for finding solutions to the leptonic sector masses and mixing. As a
case study, we accommodate the charged and neutral leptons masses and the PMNS
matrix in the 1-loop modified Zee mechanism contained in the minimal 3-3-1
model.
