  We report a measurement of the CP-violation parameter sin2beta with B^0 ->
J/psi K^0_S decays in which the J/psi decays to hadrons or to muons that do not
satisfy our standard identification criteria. With a sample of 88 million BBbar
events collected by the BaBar detector at the PEP-II asymmetric-energy $B$
factory at SLAC, we reconstruct 100 +/- 17 such events, with J/psi -> pi^+ pi^-
pi^0 being the most prevalent, and measure sin2beta = 1.56 +/- 0.42 (stat.) +/-
0.21 (syst.).
