  We consider an Abelian model with a CP-conserving Higgs potential spanned by
two complex Higgs fields. The CP invariance of the Higgs potential is then
broken explicitly beyond the Born approximation by introducing
soft-CP-violating Yukawa interactions. Based on the non-renormalization
theorem, we derive the consistency conditions under which a CP-odd counterterm
exists and, at the same time, renders the one-loop-induced mixing of a CP-even
Higgs boson with a CP-odd Higgs scalar ultra-violet finite. The novel CP-odd
tadpole renormalization may then be determined from the minimization
constraints on the Higgs potential. Finally, we discuss the phenomenological
consequences of the so-generated CP-violating scalar-pseudoscalar mixing for
the electric dipole moments of neutron, electron and muon.
