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 bou
nds 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 pseudoscal
ar, can have a high singlet content, and will be hard to detect experimenta
lly. (C) 2001 Elsevier Science B.V. All rights reserved.