  We consider spontaneous CP violation in the Next to Minimal Supersymmetric
Standard Model, without the usual $Z_3$ discrete symmetry. CP violation can
occur at tree level, raising a potential conflict with the experimental bounds
on the electric dipole moments of the electron and neutron. One escape from
this is to demand that the CP violating angles are small, but we find that this
entails a light neutral Higgs particle. This is almost pseudoscalar, can have a
high singlet content, and will be hard to detect experimentally.
