  A spontaneously-broken CP provides an alternative to the KM mechanism for CP
violation with the advantage that the strong CP problem is solved. We consider,
for such a model with a new gauged U(1), the incorporation of low-energy
supersymmetry and find the constraints on alignment and squark degeneracy. The
conclusion is that although the $\bar{\theta}$ constraints are much less severe
than in other generic schemes with supersymmetry breaking and spontaneous CP
violation, one restriction remains stronger than needed in the MSSM for
suppression of FCNC.
