  I rebuild a conventional two-Higgs doublet model by relaxing the spontaneous
CP violation and considering approximate global U(1) family symmetries. So that
the domain-wall problem does not explicitly arise at the weak scale, but CP
violation still solely originates from a single CP-phase in the vacuum after
spontaneous symmetry breaking. With this phase four types of CP-violating
mechanism are induced in the model. In particular, by a new type of the
mechanism, both the indirect- and direct- CP violation (i.e. $\epsilon$ and
$\epsilon'/\epsilon$) in kaon decay and the neutron electric dipole moment can
be consistently accommodated. The masses of the exotic scalars are weakly
constrained in the model and searching for these particles is worthwhile in the
presently accessible energy range. Substantial CP violation may occur in the
heavy quark and lepton sectors and probing their effects provides a challenge
at B-factory and colliders.
