  The angle $\gamma$ of the standard CKM unitarity triangle can be determined
from tree-level $B$-meson decays essentially without hadronic uncertainties. We
calculate the second-order electroweak corrections for the $B \to D \pi$ modes
and show that their impact on the determination of $\gamma$ could be enhanced
by an accidental cancellation of poorly known hadronic matrix elements.
However, we do not expect the resulting shift in $\gamma$ to exceed
$\big|\delta \gamma^{D\pi} /\gamma \big| \lesssim {\mathcal
O}\big(10^{-4}\big)$.
