We present a class of cancellation conditions for suppressing the total contributions of Barr-Zee diagrams to the electron electric dipole moment (eEDM). Such a cancellation is of particular significance after the new eEDM upper limit was released by the ACME Collaboration, which strongly constrains the allowed magnitude of CP violation in Higgs couplings and hence the feasibility of electroweak baryogenesis (EWBG). Explicitly, if both the CP-odd Higgs-photon-photon (Z boson) and the CP-odd Higgs-electron-positron couplings are turned on, a cancellation may occur either between the contributions of a CP-mixing Higgs boson, with the other Higgs bosons being decoupled, or between the contributions of CP-even and CP-odd Higgs bosons. With a cancellation, large CP violation in the Higgs sector is still allowed, yielding successful EWBG. The reopened parameter regions would be probed by future neutron, mercury EDM measurements, and direct measurements of Higgs CP properties at the Large Hadron Collider Run II and future colliders.