Constraining the CKM angle<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>γ</mml:mi></mml:math>and penguin contributions through combined<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mo>→</mml:mo></mml:mrow></mml:mover></mml:mrow></mml:mrow><mml:mi>π</mml:mi><mml:mi>K</mml:mi></mml:math>branching ratios

Motivated by recent CLEO measurements of $\stackrel{\ensuremath{\rightarrow}}{B}\ensuremath{\pi}K$ modes, we investigate their implications for the CKM angle $\ensuremath{\gamma}$ and a consistent description of these decays within the standard model. Interestingly it turns out that already the measurement of the combined branching ratios ${B}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}K$ and ${B}_{d}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{\mp}}{K}^{\ifmmode\pm\else\textpm\fi{}}$ allows us to derive stringent constraints on $\ensuremath{\gamma}$ 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 $\ensuremath{\gamma}=90\ifmmode^\circ\else\textdegree\fi{}$, while our method can in principle exclude a range of this kind. Consistency within the standard model implies furthermore bounds on the ratio $r\ensuremath{\equiv}|{T}^{\ensuremath{'}}|/|\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{P}|$ of the current-current and penguin operator contributions to ${B}_{d}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{\mp}}{K}^{\ifmmode\pm\else\textpm\fi{}}$, and upper limits for the $\mathrm{CP}$-violating asymmetry arising in that decay. Commonly accepted means to estimate $r$ yield values at the edge of compatibility with the present CLEO measurements.