  The $B^0_s\to D_s^\mp K^\pm$ system offers a determination of the Unitarity
Triangle angle $\gamma$. Intrigued by an LHCb analysis showing a surprisingly
large result in tension with information on the Unitarity Triangle and other
$\gamma$ measurements, we make a transparent study of the measured observables,
confirming the LHCb picture. The corresponding $\gamma$ puzzle at the $3\sigma$
level would require CP-violating contributions of New Physics, which should
also manifest themselves in the corresponding decay branching ratios. Indeed,
we find that the rates of the individual $B^0_s\to D_s^\mp K^\pm$ channels show
puzzling patterns, in accordance with similar decays, with tensions up to
$4.8\sigma$, thereby making the situation much more exciting. We present a
formalism to include New-Physics effects in a model-independent way and apply
it to the data to constrain the corresponding parameters. Interestingly, new
contributions of moderate size could accommodate the data. Utilising this
formalism in the future high-precision $B$ physics era may allow us to finally
establish new sources of CP violation.
