  Electric dipole moments (EDMs) of elementary particles and atoms probe
violations of T and P symmetries and consequently of CP if CPT is an exact
symmetry. We point out that EDMs can also serve as sensitive probes of CPT-odd,
CP-even interactions, that are not constrained by any other existing
experiments. Analyzing models with spontaneously broken Lorentz invariance, we
calculate EDMs in terms of the leading CPT-odd operators to show that
experimental sensitivity probes the scale of CPT breaking as high as
10^{12}GeV.
