  CP violation in $B^0_s$-$\bar B^0_s$ oscillations is expected at the
$10^{-5}$ level in the Standard Model but could be enhanced by New Physics.
Using $B^0_s\to D_s^-\ell^+\nu_\ell$ decays, LHCb has recently reported the new
result $(0.39\pm0.33)\times10^{-2}$ of the corresponding observable $a^s_{\rm
sl}$. We point out that other current $B$ decay data imply $a^s_{\rm sl} =
(0.004 \pm 0.075)\times10^{-2}$. In view of this strong constraint, we propose
to use $B^0_s\to D_s^-\ell^+\nu_\ell$ and similar flavor-specific decays as a
new tool to determine both the production asymmetry between $B^0_s$ and $\bar
B^0_s$ mesons, and the CP asymmetry in the subsequent $D^\pm_s$ decays. The
former serves as input for analyses of CP violation in $B^0_s$ channels, with
significant room for improvement, while the latter offers an exciting
laboratory for New Physics.
