  We study the role of a very general type of flavor symmetry in controlling
the strength of R-parity violation in supersymmetric models. We assume that
only leptons are charged under a global symmetry whose breaking induces lepton
number (and, hence, R-parity) violation. The charge assignments of leptons
under this symmetry are such that the total number of independent lepton number
violating couplings is reduced from 39 to 6. The most severe constraints on
these flavor-correlated couplings arise from neutrino masses and mixing as well
as from the non-observation of K_L -> e\mu. We find that such a scenario
predicts an almost vanishing smallest neutrino mass eigenvalue, allowing the
upcoming generation of neutrinoless double beta decay experiments to shed light
on the hierarchy.
