We report on a series of two- and three-loop calculations that were necessary to improve the theory prediction for the width difference $\Delta \Gamma_s$ in the $B_s - \bar{B}_s$ mixing. For the first time we are able to predict this important flavor observable at NNLO accuracy, which is necessary to approach the current experimental precision. Our new Standard-Model prediction obtained from the average of calculations done in the $\overline{\textrm{MS}}$ and potential subtracted (PS) schemes reads $\Delta\Gamma_s = {(0.076 \pm 0.017)} ~\mbox{ps}^{-1}$.