  We re-examine spontaneous CP violation at the tree level in the context of
the next-to-minimal supersymmetric standard model (NMSSM) with two Higgs
doublets and a gauge singlet field. We analyse the most general Higgs potential
without a discrete Z_3 symmetry, and derive an upper bound on the mass of the
lightest neutral Higgs boson consistent with present experimental data. We
investigate, in particular, its dependence on the admixture and CP-violating
phase of the gauge singlet field, as well as on tan(beta). To assess the
viability of the spontaneous CP violation scenario, we estimate epsilon_K by
applying the mass insertion approximation. We find that a non-trivial flavour
structure in the soft-breaking A terms is required to account for the observed
CP violation in the neutral kaon sector. Furthermore, combining the
minimisation conditions for spontaneous CP violation with the constraints
coming from K0-K0bar mixing, we find that the upper bound on the lightest
Higgs-boson mass becomes stronger. We also point out that the electric dipole
moments of electron and neutron are a serious challenge for SUSY models with
spontaneous CP violation.
