  In the context of the minimal supersymmetric standard model, nonzero neutrino
masses and mixing can be generated through renormalizable lepton number (and
thus R-parity) violating operators. It is examined whether neutrino mass
matrices from tree and one-loop contributions can account for two mass-squared
differences and mixing angles that explain current experimental data. By
accommodating, in particular, the solar and atmospheric neutrino data, we find
interesting restrictions not only on the free parameters of the theory, such as
lepton number violating couplings and soft-parameters, but also on the
oscillation parameters of atmospheric neutrinos.
