  We explore the Higgs sector of the Minimal Left-Right (LR) Model based on the
gauge group SU(2)_L x SU(2)_R x U(1)_{B-L} with explicit CP violation in the
Higgs potential. Since flavour-changing neutral current experiments and the
small scale of neutrino masses both place stringent constraints on the Higgs
potential, we seek to determine whether minima of the Higgs potential exist
that are consistent with current experimental bounds. We focus on the case in
which the right-handed symmetry-breaking scale is only ``moderately'' large, of
order 15-50 TeV. Unlike the case in which the Higgs potential is CP-invariant,
the CP noninvariant case does yield viable scenarios, although these require a
small amount of fine-tuning. We consider a LR model supplemented by an
additional U(1) horizontal symmetry, which results in a Higgs sector consistent
with current experimental constraints and a realistic spectrum of neutrino
masses.
