  We show that the neutrino models, as suggested by Low, which have an
additional Abelian family symmetry and a real Higgs singlet to the default
see-saw do not hinder the possibility of successful thermal leptogenesis. For
these models (neglecting radiative effects), we have investigated the situation
of strong washout in both the one-flavor approximation and when flavor effects
are included. The result is that while such models predict that theta_{13}=0
and that one light neutrino to be massless, they do not modify or provide
significant constraints on the typical leptogenesis scenario where the final
asymmetry is dominated by the decays of the lightest right-handed neutrinos.
