  Existing oscillation data point to nonzero neutrino masses with large
mixings. We analyze the generic features of the neutrino Majorana mass matrix
with inverted hierarchy and construct realistic {\it minimal schemes} for the
neutrino mass matrix that can explain the large (but not maximal) \nu_e -
\nu_mu mixing of MSW-LAM as well as the nearly maximal \nu_mu - \nu_tau mixing
and the small (or negligible) \nu_e --> \nu_tau transition. These minimal
schemes are quite unique and turn out to be extremely predictive. Implications
for neutrinoless double beta decay, tritium beta decay and cosmology are
analyzed.
