Supersymmetry withoutRparity and without lepton number

We investigate supersymmetric models where neither R parity nor lepton number is imposed. Neutrino masses can be kept highly suppressed compared to the electroweak scale if the \ensuremath{\mu} terms in the superpotential are aligned with the SUSY-breaking bilinear B terms. This situation arises naturally in the framework of horizontal symmetries. The same symmetries suppress the trilinear R-parity-violating terms in the superpotential to an acceptable level.