We present new contributions to the decay matrix element Γ q 12 of the B q −B q mixing complex, where q ¼ d or s. Our new results constitute the order α 2 s N f corrections to the penguin contributions to the Wilson coefficients entering Γ q 12 with full dependence on the charm quark mass. This is the first step toward the prediction of the CP asymmetry a q fs quantifying CP violation in mixing at next-to-next-to-leading logarithmic order (NNLO) in quantum chromodynamics (QCD) and further improves the prediction of the width difference ΔΓ q between the two neutral-meson eigenstates. We find a sizable effect from the nonzero charm mass and our partial NNLO result decreases the NLO penguin corrections to a q fs by 37% and those to ΔΓ q by 16%. We further update the Standard-Model NLO predictions for a q fs and the ratio of the width and mass differences of the B q eigenstates: If we express the results in terms of the pole mass of the bottom quark, we find a s fs ¼ ð2.07 AE 0.10Þ × 10 −5 , a d fs ¼ ð−4.71 AE 0.24Þ × 10 −4 , ΔΓ s =ΔM s ¼ ð4.33 AE 1.26Þ × 10 −3 , and ΔΓ d =ΔM d ¼ ð4.48 AE 1.19Þ × 10 −3. In the MS scheme these numbers read a s fs ¼ ð2.04 AE 0.11Þ × 10 −5 , a d fs ¼ ð−4.64 AE 0.25Þ × 10 −4 , ΔΓ s =ΔM s ¼ ð4.97 AE 1.02Þ × 10 −3 , and ΔΓ d =ΔM d ¼ ð5.07 AE 0.96Þ × 10 −3 .