  We set a preliminary 95% C.L. exclusion on the oscillation frequency of
$B_s^0 - \bar{B_s^0}$ mixing using a sample of 400,000 hadronic $Z^0$ decays
collected by the SLD experiment at the SLC during the 1996-98 run. In this
analysis, $B_s^0$ mesons are partially reconstructed by combining a fully
reconstructed $D_s$ with other $B_s^0$ decay tracks. The $D_s$ decays are
reconstructed via the $\phi \pi$ and $K^* K$ channels. The $b$-hadron flavor at
production is determined by exploiting the large forward-backward asymmetry of
polarized $Z^0 \to b \bar{b}$ decays as well as information from the hemisphere
opposite to the reconstructed B decay. The flavor of the $B_s^0$ at the decay
vertex is determined by the charge of the $D_s$. A total of 361 candidates
passed the final event selection cuts. This analysis excludes the following
values of the $B_s^0 - \bar{B_s^0}$ mixing oscillation frequency: $\Delta m_s <
1.5$ ps$^{-1}$, $2.6 < \Delta m_s < 4.9$ ps$^{-1}$, and $10.8 < \Delta m_s <
13.5$ ps$^{-1}$ at the 95% confidence level.
