  Predictions of the Cabibbo-Kobayashi-Maskawa (CKM) parameters are
investigated in detail in recent predictive models which are based on
low-energy non-abelian discrete family symmetries. Some of the models can
already be excluded at the present precision of the determination of the CKM
parameters, while some of them seem to survive. We find that to make the
uncertainties in the predictions comparable with the assumed uncertainties of
$\sim 1^{\circ}$ and $\sim 2^{\circ}$ in $\phi_2$ and $\phi_3$, respectively,
at about 50 inverse atto barn achieved at a feature B factory, it is necessary
to reduce the uncertainties in the quark masses, especially that of the strange
quark mass by more than 60%.
