Abstract: We discuss a theorem of Csonka, Moravcsik, and Scadron on the nonexistence of purely kinematic parity experiments involving scattering processes with more than four particles. Such experiments can be carried out, even in the case of noncoplanar momenta in the center of mass frame, if the experimenter can construct coherent superpositions of some asymptotic states and their parity inverses, as one ideally supposes. If such information is not available, the result of Csonka, Moravcsik, and Scadron appears to stand.