The decays B-d --> pi(-/+)K(+/-) and B+/- --> pi(+/-)K provide interesting constraints on the angle gamma of the unitarity triangle of the CKM matrix. It is shown that bounds on gamma can also be obtained from the time evolution of untagged B-s --> K+K- and B-s --> K-0(K) over bar(0) decays, provided the B-s system exhibits a sizable width difference Delta T-s. A detailed discussion of rescattering processes and electroweak penguin effects, which limit the theoretical accuracy of these constraints, and of methods to control them through experimental data is given. Moreover, strategies an pointed out to go beyond these bounds by relating the B-u,B- (d) --> pi K and untagged B-s --> K (K) over bar decays through the SU(3) flavor symmetry of strong interactions. If a tagged, time-dependent measurement of the B-s --> K+K- and B-s --> K-0(K) over bar(0) modes should become possible, gamma could be determined from the corresponding observables in a way that makes use of only the SU(2) isospin symmetry and takes into account rescattering effects "automatically." The impact of new-physics contributions to B-s(0) - (B) over bar(s)(0) mixing is also analyzed, and interesting features arising in such a scenario of physics beyond the standard model are pointed out. [S0556-2821(98)02519-3].