  The B_s^0 -> J/psi K_S decay has recently been observed by the CDF
collaboration and will be of interest for the LHCb experiment. This channel
will offer a new tool to extract the angle gamma of the unitarity triangle and
to control doubly Cabibbo-suppressed penguin corrections to the determination
of sin(2beta) from the well-known B_d^0 -> J/psi K_S mode with the help of the
U-spin symmetry of strong interactions. While any competitive determination of
gamma is interesting, the latter aspect is particularly relevant as LHCb will
enter a territory of precision which makes the control of doubly
Cabibbo-suppressed Standard-Model corrections mandatory. Using the data from
CDF and the e^+e^- B factories as a guideline, we explore the sensitivity for
gamma and the penguin parameters and point out that the B_s^0-\bar B_s^0 mixing
phase phi_s, which is only about -2 deg in the Standard Model but may be
enhanced through new physics, is a key parameter for these analyses. We find
that the mixing-induced CP violation S(B_s^0 -> J/psi K_S) shows an interesting
correlation with sin(phi_s), which serves as a target region for the first
measurement of this observable at LHCb.
