  We examine the neutrino mass matrix in the version of Zee model where both
Higgs doublets couple to the leptons. We show that in this case one can
accommodate the large mixing angle (LMA) MSW solution of the solar neutrino
problem, while avoiding maximal solar mixing and conflicts with constraints on
lepton family number-violating interactions. In the simplified scenario we
consider, we have the neutrino mass spectrum characterized by $m_1 \simeq m_2
\simeq \sqrt{\Delta m^2_\mathrm{atm}}/\sin 2\theta$ and $m_3/m_1 \simeq \cos
2\theta$, where $\theta$ is the solar mixing angle.
