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
{\it 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.