  To help the difficult determination of the angle $\gamma$ of the unitarity
triangle, Aleksan, Dunietz and Kayser have proposed the modes of the type
$K^-D^+_s$, common to $B_s$ and $\bar{B}_s$. We point out that it is possible
to gain in statistics by a sum over all modes with ground state mesons in the
final state, i.e. $K^-D^+_s$, $K^{*-}D_+^s$, $K^-D^{*+}_s$, $K^{*-}D^{*+}_s$.
The delicate point is the relative phase of these different contributions to
the dilution factor $D$ of the time-dependent asymmetry. Each contribution to
$D$ is proportional to a product $F^{cb}$ $F^{ub}$ $f_{D_s}$ $f_K$ where $F$
denotes form factors and $f$ decay constants. Within a definite phase
convention, lattice calculations do not show any change in sign when
extrapolating to light quarks the form factors and decay constants. Then, we
can show that all modes contribute constructively to the dilution factor,
except the $P$-wave $K^{*-}D^{*+}_s$, which is small. Quark model arguments
based on wave function overlaps also confirm this stability in sign. By summing
over all these modes we find a gain of a factor 6 in statistics relatively to
$K^-D^+_s$. The dilution factor for the sum $D_{tot}$ is remarkably stable for
theoretical schemes that are not in very strong conflict with data on $B \to
\psi K(K^*)$ or extrapolated from semileptonic charm form factors, giving
$D_{tot} \geq 0.6$, always close to $D(K^- D^+_s)$.
