  In the recent literature, constraints on the CKM angle $\gamma$ arising from
the branching ratios for $B^\pm\to\pi^\pm K$ and $B_d\to\pi^\mp K^\pm$ decays
received a lot of attention. An important theoretical limitation of the
accuracy of these bounds is due to rescattering effects, such as
$B^+\to\{\pi^0K^+\}\to\pi^+K^0$. We point out that these processes are related
to penguin topologies with internal up quark exchanges and derive SU(2) isospin
relations among the $B^+\to\pi^+K^0$ and $B_d^0\to\pi^-K^+$ decay amplitudes by
defining ``tree'' and ``penguin'' amplitudes in a proper way, allowing the
derivation of generalized bounds on the CKM angle $\gamma$. We propose
strategies to obtain insights into the dynamics of penguin processes with the
help of the decays $B_{u,d}\to K\bar{K}$ and $B^\pm\to\pi^\pm K$, derive a
relation among the direct CP-violating asymmetries arising in these modes, and
emphasize that rescattering effects can be included in the generalized bounds
on $\gamma$ completely this way. Moreover, we have a brief look at the impact
of new physics.
