  New physics contributions to B_s-\bar{B}_s mixing can be parametrized by the
size (r_s^2) and the phase (2\theta_s) of the total mixing amplitude relative
to the Standard Model amplitude. The phase has so far been unconstrained. We
first use the D0 measurement of the semileptonic CP asymmetry A_SL to obtain
the first constraint on the semileptonic CP asymmetry in B_s decays,
A_SL^s=-0.008 \pm 0.011. Then we combine recent measurements by the CDF and D0
collaborations - the mass difference (\Delta M_s), the width difference
(\Delta\Gamma_s) and A_SL^s - to constrain 2\theta_s. The errors on
\Delta\Gamma_s and A_SL^s should still be reduced to have a sensitive probe of
the phase, yet the central values are such that the regions around 2\theta_s ~
3\pi/2 and, in particular, 2\theta_s ~ \pi/2, are disfavored.
