  A new optical pumping scheme is presented that uses incoherent Raman
transitions to prepare a trapped Cesium atom in a specific Zeeman state within
the 6S_{1/2}, F=3 hyperfine manifold. An important advantage of this scheme
over existing optical pumping schemes is that the atom can be prepared in any
of the F=3 Zeeman states. We demonstrate the scheme in the context of cavity
quantum electrodynamics, but the technique is equally applicable to a wide
variety of atomic systems with hyperfine ground-state structure.
