We systematically analyze constraints on supersymmetric theories imposed by
the experimental bounds on the electron, neutron, and mercury electric dip
ole moments. We critically reappraise the known mechanisms to suppress the
EDMs and conclude that only the scenarios with approximate CP-symmetry or f
lavour-off-diagonal CP violation remain attractive after the addition of th
e mercury EDM constraint. (C) 2001 Elsevier Science B.V. All rights reserve
d.