  The three neutrino Zee model and its extension including three active and one
sterile species are studied in the light of new neutrino oscillation data. We
obtain analytical relations for the mixing angle in solar oscillations in terms
of neutrino mass squared differences. For the four neutrino case, we obtain the
result $\mathsf{sin^2 2 \theta_\odot \approx 1 - [ (\Delta m^2_{Atm})^2/(4
\Delta m^2_{LSND} \Delta m^2_\odot) ]^2}$, which can accommodate both the large
and small mixing scenarios. We show that within this framework, while both the
SMA-MSW and the LMA-MSW solutions can easily be accommodated, it would be
difficult to reconcile the LOW-QVO solutions. We also comment on the
active-sterile admixture within phenomenologically viable textures.
