  The Minimal Supersymmetric Standard Model can possess several CP-violating
phases beyond the conventional Cabibo-Kobayashi-Maskawa phase. We calculate the
contribution of these phases to T-violating nuclear forces. These forces induce
a Schiff moment in the $^{199}$Hg nucleus, which is strongly limited by
experiments aimed at the detection of the electric dipole moment of the mercury
atom. The result for $d_{Hg}$ is found to be very sensitive to the CP-violating
phases of the MSSM and the calculation carries far fewer QCD uncertainties than
the corresponding calculation of the neutron EDM. In certain regions of the
MSSM parameter space, the limit from the mercury EDM is stronger than previous
constraints based on either the neutron or electron EDMs. We present combined
constraints from the mercury and electron EDMs to limit both CP-violating
phases of the MSSM. We also present limits in mSUGRA models with unified
gaugino and scalar masses at the GUT scale.
