  We present a two-Higgs-doublet model, with a $\mathbbm{Z}_3$ symmetry, in
which CP violation originates solely in a soft (dimension-2) coupling in the
scalar potential, and reveals itself solely in the CKM (quark mixing) matrix.
In particular, in the mass basis the Yukawa interactions of the neutral scalars
are all real. The model has only eleven parameters to fit the six quark masses
and the four independent CKM-matrix observables. We find regions of parameter
space in which the flavour-changing neutral couplings are so suppressed that
they allow the scalars to be no heavier than a few hundred GeV.
