A new ‘harmonic’ BRST method is presented for quantizing those dynamical systems having second-class constraints which split into holomorphic and antiholomorphic algebras. These theories include those whose phase spaces are coadjoint orbits of a compact semisimple Lie group. The method also applies to theories with holomorphic first-class constraints which have nonvanishing brackets with their antiholomorphic conjugates. An operatorial quantization, resembling supersymmetric quantum mechanics, is presented. In addition, a general path integral is given and is shown to reduce to that given by Batalin, Fradkin, and Vilkovisky.