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Supersymmetric theories allow a variety of sources for CP violation. Radiative contributions to ϵ, ϵ′, p and the neutron electric dipole moment are considered in two versions of the minimal N= 1 supergravity theory. If the top quark is heavy, the superbox may dominate ϵ and limit s 2 s 3 s δ, thus suppressing contributions of s δ to ϵ′. Possibly large contributions to ϵ′ are considered which are independent of δ. An additional large contribution to the electric dipole moment of the neutron is pointed out. A proposal is put forward that may lead to a solution to the strong CP problem.