We describe optically pumping a beam of sodium atoms to >96% mS and >92% mS, mI state selection. (We have accurately measured the population of every mS, mI state in the optically pumped beam.) For the optical pumping both ground hyperfine states are pumped, using single-mode cw dye-laser radiation tuned to the 3S1/2–3P1/2 transition that is phase modulated in a LiTaO3 crystal to produce first-order sidebands at approximately the 1772-MHz hyperfine splitting of the ground state. The z-directed optical pumping is performed in a z-directed magnetic field of ~5 G. The state-selected atoms then move, in ~1 cm, into an ~200 G, z-directed field. The downstream probe laser beam is scanned through the 3S1/2 (mS, mI) → 3P3/2 (mS′, mI) transitions, which are spectroscopically resolved at 200 G, and the fluorescence intensities portray the residual populations in each of the eight 3S1/2 states.