  CP-violating effects in the time-dependent angular distribution of the B^0_s
-> J/psi[-> ell^+ ell^-] phi[-> K^+K^-] decay products play a key role for the
search of new physics. The hadronic Standard-Model uncertainties are related to
doubly Cabibbo-suppressed penguin contributions and are usually assumed to be
negligibly small. In view of recent results from the Tevatron and the quickly
approaching start of the data taking at the LHC, we have a critical look at the
impact of these terms, which could be enhanced through long-distance QCD
phenomena, and explore the associated uncertainty for the measurement of the
CP-violating B^0_s-\bar B^0_s mixing phase. We point out that these effects can
actually be controlled by means of an analysis of the time-dependent angular
distribution of the B^0_s -> J/psi[-> ell^+ ell^-] \bar K^{*0}[-> pi^+ K^-]
decay products, and illustrate this through numerical studies. Moreover, we
discuss SU(3)-breaking effects, which limit the theoretical accuracy of our
method, and suggest internal consistency checks of SU(3).
