  We revisit the minimal supersymmetric left-right model with B-L=2 triplet
Higgs fields and show that a self-consistent picture emerges with automatic
R-parity conservation even in the absence of higher dimensional operators. By
computing the effective potential for the Higgs system including heavy Majorana
neutrino Yukawa couplings we show that the global minimum of the model can lie
in the charge and R-parity conserving domain. The model provides natural
solutions to the SUSY phase problem and the strong CP problem and makes several
interesting predictions. Quark mixing angles arise only after radiative
corrections from the lepton sector are taken into account. A pair of doubly
charged Higgs fields remain light below TeV with one field acquiring its mass
entirely via renormalization group corrections. We find this mass to be not
much above the Bino mass. In the supergravity framework for SUSY breaking, we
also find similar upper limits on the stau masses. Natural solutions to the
$\mu$ problem and the SUSY CP problem entails light SU(2)_L triplet Higgs
fields, leading to rich collider phenomenology.
