  The recently reported measurements of the CP asymmetry a(psi K) by the BABAR
and BELLE collaborations are in good agreement with the standard model
prediction. With the anticipated precision in a(psi K) at the B factories and
hadron colliders, one hopes to pin down any possible deviation from the SM. We
discuss an extension of the MFV-supersymmetric models which comfortably
accommodates the current measurements of the CP asymmetry a(psi K), but differs
from the SM due to an additional flavour changing structure beyond the CKM
matrix. We analyze the compatibility of this model with present data and
suggest specific tests in forthcoming experiments in B physics. In addition to
the CP-asymmetries in B-meson decays and the Bs-bar(Bs) mass difference, we
emphasize measurements of the radiative transition b -> d gamma as sensitive
probes of the postulated flavour changing structure. Interestingly, the
CKM-unitarity analysis in these models also allows solutions with gamma > pi/2,
where gamma=-arg(Vub). Such large values of gamma are hinted by the current
measurements of the branchig ratios for the decays B -> pi pi and B -> K pi.
