The decay rates for B-0 --> K(+)pi(-), B+ --> K(0)pi(+), and the charge-conjugate processes were found to provide information on the weak phase gamma=Arg(V-ub(*)) when the ratio r of weak tree and penguin amplitudes was taken from data on B --> pi pi or semileptonic B --> pi decays. We show here that the rates for B-s --> K(-)pi(+) and (B) over bar(s) --> K(+)pi(-) can provide the necessary information on r, and estimate the statistical accuracy of forthcoming measurements at the Fermilab Tevatron. (C) 2000 Elsevier Science B.V. All rights reserved.