We consider two-loop QCD corrections to the element $$ {\Gamma}_{12}^q $$
Γ
12
q
of the decay matrix in Bq−$$ {\overline{B}}_q $$
B
¯
q
mixing, q = d, s, in the leading power of the Heavy Quark Expansion. The calculated contributions involve one current-current and one penguin operator and constitute the next step towards a theory prediction for the width difference ∆Γs matching the precise experimental data. We present compact analytic results for all matching coefficients in an expansion in mc/mb up to second order. Our new corrections are comparable in size to the current experimental error and slightly increase ∆Γs.