  We elaborate on an earlier proposal by Ernest Ma of a type II seesaw
mechanism for suppressing the vacuum expectation values of some Higgs doublets.
We emphasize that, by nesting this form of seesaw mechanism into various other
seesaw mechanisms, one may obtain light neutrino masses in such a way that the
new-physics scale present in the seesaw mechanism - the masses of scalar
gauge-SU(2) triplets, scalar SU(2) doublets, or right-handed neutrinos - does
not need to be higher than a few 10 TeV. We also investigate other usages of
the type II seesaw mechanism for Higgs doublets. For instance, the suppression
of the vacuum expectation values of Higgs doublets may realize Froggatt-Nielsen
suppression factors in some entries of the fermion mass matrices.
