  We present a general parametrization of $B^\pm\to\pi^\pm K, \pi^0K^\pm$ and
$B_d\to\pi^0 K, \pi^\mp K^\pm$ decays, taking into account both electroweak
penguin and rescattering effects. This formalism allows -- among other things
-- an improved implementation of the strategies that were recently proposed by
Neubert and Rosner to probe the CKM angle $\gamma$ with the help of
$B^\pm\to\pi^\pm K, \pi^0K^\pm$ decays. In particular, it allows us to
investigate the sensitivity of the extracted value of $\gamma$ to the basic
assumptions of their approach. We find that certain SU(3)-breaking effects may
have an important impact and emphasize that additional hadronic uncertainties
are due to rescattering processes. The latter can be controlled by using SU(3)
flavour symmetry arguments and additional experimental information provided by
$B^\pm\to K^\pm K$ modes. We propose a new strategy to probe the angle $\gamma$
with the help of the neutral decays $B_d\to\pi^0 K, \pi^\mp K^\pm$, which is
theoretically cleaner than the $B^\pm\to\pi^\pm K, \pi^0K^\pm$ approach. Here
rescattering processes can be taken into account by just measuring the
CP-violating observables of the decay $B_d\to\pi^0K_{\rm S}$. Finally, we point
out that an experimental analysis of $B_s\to K^+K^-$ modes would also be very
useful to probe the CKM angle $\gamma$, as well as electroweak penguins, and we
critically compare the virtues and weaknesses of the various approaches
discussed in this paper. As a by-product, we point out a strategy to include
the electroweak penguins in the determination of the CKM angle $\alpha$ from
$B\to\pi\pi$ decays.
