I review the status of the Standard-Model prediction of the width difference
$\Delta\Gamma_s$ among the two $B_s$ meson eigenstates. Ongoing effort addresses
three-loop QCD corrections, corresponding to the next-to-next-to-leading
order of QCD. With an improved theoretical precision of the ratio $\Delta\Gamma_s/\Delta M_s$,
where $\Delta M_s$ denotes the mass difference in the $B_s$-$\bar B_s$ system,
one can probe new physics in $\Delta M_s$ without sensitivity to $|V_{cb}|$,
whose value is currently controversial.