  Present experiments in pursuit of the mass difference in the Bs-Bs(bar)
system have put a lower bound on this quantity of $\Delta M_s > 14.9 ps^{-1}$
(at 95% C.L.). The same experiments also yield a local minimum in the
log-likelihood function around $\Delta M_s = 17.7 ps^{-1}$, which is
$2.5\sigma$ away from being zero. Motivated by these observations, we
investigate the consequences of a possible measurement of $\Delta M_s = 17.7
\pm 1.4 ps^{-1}$, in the context of both the standard model and supersymmetric
models with minimal flavor violation. We perform a fit of the quark mixing
parameters in these theories and estimate the expected ranges of the CP
asymmetries in B decays, characterized by $\alpha$, $\beta$ and $\gamma$, the
interior angles of the CKM-unitarity triangle. Based on this study, we argue
that, if indeed $\Delta M_s$ turns out to be in its currently-favored range,
this would disfavor a large class of supersymmetric models. Indeed, of all the
models examined here, the best fit to the data occurs for the standard model.
