  We present a simple and predictive model of radiative neutrino masses. It is
a special case of the Zee model which introduces two Higgs doublets and a
charged singlet. We impose a family-dependent Z_4 symmetry acting on the
leptons, which reduces the number of parameters describing neutrino
oscillations to four. A variety of predictions follow: The hierarchy of
neutrino masses must be inverted; the lightest neutrino mass is extremely small
and calculable; one of the neutrino mixing angles is determined in terms of the
other two; the phase parameters take CP-conserving values with \delta_{CP} =
\pi; and the effective mass in neutrinoless double beta decay lies in a narrow
range, m_{\beta \beta} = (17.6 - 18.5) meV. The ratio of vacuum expectation
values of the two Higgs doublets, tan\beta, is determined to be either 1.9 or
0.19 from neutrino oscillation data. Flavor-conserving and flavor-changing
couplings of the Higgs doublets are also determined from neutrino data. The
non-standard neutral Higgs bosons, if they are moderately heavy, decay
dominantly into \mu and \tau with prescribed branching ratios. Observable rates
for the decays \mu \to e \gamma and \tau \to 3\mu are predicted if these
scalars have masses in the range of 150-500 GeV.
