We discuss some problems associated with obtaining an atomic beam with a large fraction of excited−state atoms. We show, e.g., that for sodium atoms to be pumped up into the 32P1/2state, they must experience a minimum of three optical frequencies near theD1line. In order to achieve this with only one optical frequency, the following method is proposed: A strong laser beam impinges three times on an atomic beam, each time under a different angle, in such a way that for one velocity class the Doppler shift generates the three frequencies needed. The effects of the polarization of the laser beams are discussed.