  It has recently been pointed out that the observables of the decay $B^+\to
K^+\bar{K^0}$ and its charge conjugate allow us to take into account
rescattering effects in constraints on the CKM angle $\gamma$ arising from
$B^\pm\to\pi^\pm K$ and $B_d\to\pi^\pm K^\pm$ modes, and that they play an
important role to obtain insights into final-state interactions. In this paper,
the formalism needed to accomplish this task is discussed in detail.
Furthermore, using a transparent model to describe the rescattering processes,
as well as electroweak penguins, we calculate the quantities parametrizing the
$B^+\to\pi^+ K^0$ and $B_d^0\to\pi^- K^+$ decay amplitudes for specific
examples, and illustrate the constraints on $\gamma$ arising from the
corresponding observables. Although this model is very crude, it shows nicely
the power of $B^\pm\to K^\pm K$ both to include the rescattering effects in the
bounds on $\gamma$ and to obtain insights into final-state interactions.
Moreover this model exhibits the interesting feature that the combined
branching ratio BR$(B^\pm\to K^\pm K)$ may be considerably enhanced through
rescattering processes, as was recently pointed out within a general framework.
