  Recently, the CDF and D0 collaborations measured indirect CP violation in Bs
-> J/psi phi and found a hint of a signal. If taken at face value, this can be
interpreted as a nonzero phase of Bs-Bsbar mixing (beta_s), in disagreement
with the standard model, which predicts that beta_s ~= 0. In this paper, we
argue that this analysis may be incomplete. In particular, there can be new
physics (NP) in the bbar -> sbar c cbar decay. If so, the value of beta_s is
different than for the case in which NP is assumed to be present only in the
mixing. We have examined several models of NP and found that, indeed, there can
be significant contributions to the decay. These effects are consistent with
measurements in B -> J/psi K* and Bd -> J/psi Ks. Due to the NP in the decay,
polarization-dependent indirect CP asymmetries and triple-product asymmetries
are predicted in Bs -> J/psi phi.
