In the heavy-quark limit, the hadronic matrix elements entering nonleptonic B-meson decays into two light mesons can be calculated from first principles including "nonfactorizable" strong-interaction corrections. The B→πK, ππ decay amplitudes are computed including electroweak penguin contributions, SU(3) violation in the light-cone distribution amplitudes, and an estimate of power corrections from chirally-enhanced terms and annihilation graphs. The results are then used to reduce the theoretical uncertainties in determinations of the weak phases γ and α. In that way, new constraints in the ( ρ̄, η̄) plane are derived. Predictions for the B→πK, ππ branching ratios and CP asymmetries are also presented. A good global fit to the (in part preliminary) experimental data on the branching fractions is obtained without taking recourse to phenomenological models.