  Electric dipole moments constitute highly sensitive probes for CP-violating
effects beyond the Standard Model. The upper limits obtained in various
precision experiments can therefore be used to strongly restrict new physics
models. However, relating the experimental information to parameters of a
specific model is complicated by the presence of various sources for EDMs as
well as large theory uncertainties in some of the relevant matrix elements. In
this article, we address both issues for the EDMs of heavy paramagnetic
systems, where it is possible to include subleading contributions, thereby
model-independently extracting the electron EDM. We furthermore use expressions
for the presently phenomenologically relevant EDMs with conservative estimates
for the theoretical uncertainties to place constraints on CP-violating phases
in the context of Two-Higgs-Doublet models.
