We investigate supersymmetric models where neither R parity nor lepton
number is imposed. Neutrino masses can be kept highly suppressed comp
ared to the electroweak scale if the mu terms in the superpotential ar
e aligned with the SUSY-breaking bilinear B terms. This situation aris
es naturally in the framework of horizontal symmetries. The same symme
tries suppress the trilinear R-parity-violating terms in the superpote
ntial to an acceptable level.