  The decay rates for $B^0 \to K^+ \pi^-$, $B^+ \to K^0 \pi^+$, and the
charge-conjugate processes were found to provide information on the weak phase
$\gamma \equiv {\rm Arg}(V_{ub}^*)$ when the ratio $r$ of weak tree and penguin
amplitudes was taken from data on $B \to \pi \pi$ or semileptonic $B \to \pi$
decays. We show here that the rates for $B_s \to K^- \pi^+$ and $\bar B_s \to
K^+ \pi^-$ can provide the necessary information on $r$, and estimate the
statistical accuracy of forthcoming measurements at the Fermilab Tevatron.
