We construct phenomenologically viable supersymmetric models where CP is an approximate symmetry. The full high energy theory has exact CP and horizontal symmetries that are spontaneously broken with a naturally induced hierarchy of scales, Λ C P Λ H . Consequently, the effective low energy theory, i.e. the supersymmetric Standard Model, has CP broken explicitly but by a small parameter. The K parameter is accounted for by supersymmetric contributions. The predictions for other CP-violating observables are very different from the Standard Model. In particular, CP-violating effects in neutral B decays into final CP eigenstates such as B -> ψK S and in K -> πvv decays are very small.