  We build a class of two-Higgs-doublet models in which the flavour-changing
couplings of the neutral scalars are related in an exact way to elements of the
quark mixing matrix. In this framework, we explore the different possibilities
for CP violation and find some interesting scenarios, like a realization of the
superweak idea without CP violation in the $B$-meson system. In another
scenario the neutral scalars can be relatively light, and their contributions
to the $B^0$--$\bar{B}^0$ transitions can alter the standard-model predictions
for CP violation in that system.
