  Motivated by recent CLEO measurements of $B\to\pi K$ modes, we investigate
their implications for the CKM angle $\gamma$ and a consistent description of
these decays within the Standard Model. Interestingly it turns out that already
the measurement of the combined branching ratios $B^\pm\to\pi^\pm K$ and
$B_d\to\pi^\mp K^\pm$ allows to derive stringent constraints on $\gamma$ which
are complementary to the presently allowed range for that angle. This range,
arising from the usual fits of the unitarity triangle, is typically symmetric
around $\gamma = 90^\circ$, while our method can in principle exclude a range
of this kind. Consistency within the Standard Model implies furthermore bounds
on the ratio $r\equiv|T'|/|\tilde P|$ of the current-current and penguin
operator contributions to $B_d\to\pi^\mp K^\pm$, and upper limits for the
CP-violating asymmetry arising in that decay. Commonly accepted means to
estimate $r$ yield values at the edge of compatibility with the present CLEO
measurements.
