  We present a Zee model with a family dependent $Z_2$ symmetry for radiative
neutrino masses. Our motivation is to get a model that correctly describes
neutrino oscillation phenomena, while at the same time offers definite
predictions. The imposed $Z_2$ symmetry greatly reduces the number of free
parameters in the model. These parameters are then determined from the neutrino
data, from which one can study its outcomes. Our setup only admits
quasidegenerate neutrino masses with the sum of neutrino masses between 100 and
130 meV, the effective Majorana mass between 20 and 40 meV, and the effective
electron neutrino mass between 48 and 53 meV. The ratio of the vacuum
expectation values of the Higgs doublets, $\tbeta$, is found to be
$\tbeta\lesssim 0.5$ and $\tbeta\gtrsim 10$. The former is ruled out by lepton
flavor violation (LFV) processes, such as $\mu\to e\gamma$ and $\mu\to e$
conversion, which are determined up to two loops. For the latter, these LFV
processes are within reach of the next generation of experiments. Moreover, for
$\tbeta\gtrsim10$, the couplings of heavy neutral scalars to dimuon are
significant. If they are sufficiently light, i.e., $\lesssim200$ GeV, collider
search for their decays into muon pair provides a stronger constraint on most
parts of the model parameter space than the LFV ones.
