  We study the impact of the Randall-Sundrum setup on the width difference
$\Delta\Gamma_s$ and the CP-violating phase $\phi_s$ in the $\bar
B_s^0$-$B_s^0$ system. Our calculations are performed in the general framework
of an effective theory, based on operator product expansion. The result can
thus be used for many new physics models. We find that the correction to the
magnitude of the decay amplitude $\Gamma_{12}$ is below 4% for a realistic
choice of input parameters. The main modification in the
$\Delta\Gamma_s/\beta_s$-plane is caused by a new CP-violating phase in the
mixing amplitude, which allows for a better agreement with the experimental
results of CDF and D\O from $B_s^0\rightarrow J/\psi\phi\,$ decays. The
best-fit value of the CP asymmetry $S_{\psi\phi}$ can be reproduced, while
simultaneously the theoretical prediction for the semileptonic CP asymmetry
$A_{\rm SL}^s$ can enter the $1\sigma$ range.
