  Direct CP violation in B -> J/Psi K is a clean test for new physics. However,
the direct CP asymmetry will vanish if the new-physics amplitude has the same
strong phase as the standard-model amplitude. We show that this type of new
physics can still be detected via an angular analysis of the sister decay mode
B -> J/Psi K^*. Time-dependent measurements and tagging are not necessary.
Should new physics be found, this angular analysis can be used to obtain
information about the size of the new-physics parameters.
