  The Standard Model predicts a large width difference in the $B_s$ system. New
physics can contribute significantly to the {\it mass} difference. If this
contribution is CP violating, this will always result in a reduction of the
{\it width} difference. The analyses of measurements of the width difference
using $B_s$ decays into CP eigenstates have to be modified in the presence of
new physics. We discuss how the width difference and the new CP violating phase
in $B_s$ mixing can be measured.
