  Evidence for neutrino oscillations is pointing to the existence of tiny but
finite neutrino masses. Such masses may be naturally generated via radiative
corrections in models such as the Zee model where a singlet Zee-scalar plays a
key role. We minimally extend the Zee model by including a right-handed singlet
neutrino \nu_R. The radiative Zee-mechanism can be protected by a simple U(1)_X
symmetry involving only the \nu_R and a Zee-scalar. We further construct a
class of models with a single horizontal U(1)_FN (a la Frogatt-Nielsen) such
that the mass patterns of the neutrinos and leptons are naturally explained. We
then analyze the muon anomalous magnetic moment (g-2) and the flavor changing
\mu --> e\gamma decay. The \nu_R interaction in our minimal extension is found
to induce the BNL g-2 anomaly, with a light charged Zee-scalar of mass 100-300
GeV.
