  We revisit the constraints imposed by electric dipole moments (EDMs) of
nucleons and heavy atoms on new CP-violating sources within supersymmetric
theories. We point out that certain two-loop renormalization group corrections
induce significant mixing between the basis-invariant CP-odd phases. In the
framework of the constrained minimal supersymmetric standard model (CMSSM), the
CP-odd invariant related to the soft trilinear A-phase at the GUT scale,
theta_A, induces non-trivial and distinct CP-odd phases for the three gaugino
masses at the weak scale. The latter give one-loop contributions to EDMs
enhanced by tan beta, and can provide the dominant contribution to the electron
EDM induced by theta_A. We perform a detailed analysis of the EDM constraints
within the CMSSM, exhibiting the reach, in terms of sparticle spectra, which
may be obtained assuming generic phases, as well as the limits on the CP-odd
phases for some specific parameter points where detailed phenomenological
studies are available. We also illustrate how this reach will expand with
results from the next generation of experiments which are currently in
development.
