  We present a detailed study of the Thallium, neutron, Mercury and deuteron
electric dipole moments (EDMs) in the CP-violating Minimal Supersymmetric
extension of the Standard Model (MSSM). We take into account the complete set
of one-loop graphs, the dominant Higgs-mediated two-loop diagrams, the complete
CP-odd dimension-six Weinberg operator and the Higgs-mediated four-fermion
operators. We improve upon earlier calculations by including the resummation
effects due to CP-violating Higgs-boson mixing and to threshold corrections to
the Yukawa couplings of all up- and down-type quarks and charged leptons. As an
application of our study, we analyse the EDM constraints on the CPX, trimixing
and Maximally CP- and Minimally Flavour-Violating (MCPMFV) scenarios.
Cancellations may occur among the CP-violating contributions to the three
measured EDMs arising from the 6 CP-violating phases in the MCPMFV scenario,
leaving open the possibility of relatively large contributions to other
CP-violating observables. The analytic expressions for the EDMs are implemented
in an updated version of the code CPsuperH2.0.
