  Theories in which neutrino masses are generated by a conventional see-saw
mechanism generically yield masses which are O(v^2) in units where M_{Pl}=1,
which is naively too small to explain the results from SuperKamiokande. In
supersymmetric theories with gravity mediated supersymmetry breaking, the
fundamental small parameter is not v/M_{Pl}, but m_I/M_{Pl}, where m_I is the
scale of supersymmetry breaking in the hidden sector. We note that
m_I^3/M_{Pl}^2 is only slightly too large to explain SuperKamiokande, and
present two models that achieve neutrino masses at this order in m_I, one of
which has an additional suppression lambda_tau^2, while the other has
additional suppression arising from a loop factor. The latter model shares a
great deal of phenomenology with a class of models previously explored,
including the possibility of viable sneutrino dark matter.
