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The three neutrino Zee model and its extension including three active and onesterile species are studied in the light of new neutrino oscillation data. Weobtain analytical relations for the mixing angle in solar oscillations in termsof neutrino mass squared differences. For the four neutrino case, we obtain theresult $\mathsf{sin^2 2 \theta_\odot \approx 1 - [ (\Delta m^2_{Atm})^2/(4\Delta m^2_{LSND} \Delta m^2_\odot) ]^2}$, which can accommodate both the largeand small mixing scenarios. We show that within this framework, while both theSMA-MSW and the LMA-MSW solutions can easily be accommodated, it would bedifficult to reconcile the LOW-QVO solutions. We also comment on theactive-sterile admixture within phenomenologically viable textures.Comment: The paper has been substantially rewritten, especially in Section IV,  though the basic results are unchanged. Some new references and an appendix  have been adde

Constraints on radiative neutrino mass models from oscillation data