We systematically analyze constraints on supersymmetric theories imposed by the experimental bounds on the electron, neutron, and mercury electric dipole moments. We critically reappraise the known mechanisms to suppress the EDMs and conclude that only the scenarios with approximate CP-symmetry or flavour-off-diagonal CP violation remain attractive after the addition of the mercury EDM constraint.
Abel, S., Khalil, S., & Lebedev, O. (2001). EDM constraints in supersymmetric theories. Nuclear Physics B, 606(1-2), 151-182. https://doi.org/10.1016/s0550-3213%2801%2900233-4