  We consider several low energy consequences arising from a class of
supersymmetric models based on the gauge groups $SU(2)_L\times SU(2)_R \times
U(1)_{B-L}$ and $SU(4)_C\times SU(2)_L \times SU(2)_R$ in which the gauge
hierarchy and $\mu$ problems have been resolved. There are important
constraints on the MSSM parameters $\tan \beta (\simeq m_t/m_b)$, $B$ and
$\mu$, and we discuss how they are reconciled with radiative electroweak
breaking. We also consider the ensuing sparticle and Higgs spectroscopy, as
well as the decays $b\to s \gamma$ and $\mu \to e \gamma$. The latter process
may be amenable to experimental tests through an order of magnitude increase in
sensitivity.
