  The interpretation of the baryon asymmetry of the Universe necessitates the
CP violation beyond the Standard Model (SM). We present a general cancellation
mechanism in the theoretical predictions of the electron electric dipole
moments (EDM), quark chromo-EDMs, and Weinberg operators. A relative large CP
violation in the Higgs sector is allowed by the current electron EDM constraint
released by the ACME collaboration in 2013, and the recent $^{199}$Hg EDM
experiment. The cancellation mechanism can be induced by the mass splitting of
heavy Higgs bosons around $\sim\mathcal{O}(0.1-1)$ GeV, and the extent of the
mass degeneracy determines the magnitude of the CP-violating phase. We
explicate this point by investigating the CP-violating two-Higgs-doublet model
and the minimal supersymmetric Standard Model. The cancellation mechanism is
general when there are CP violation and mixing in the Higgs sector of new
physics models. The CP-violating phases in this scenario can be excluded or
detected by the projected $^{225}$Ra EDM experiments with precision reaching
$\sim10^{-28}\,e\cdot{\rm cm}$, as well as the future colliders.
