A novel multichannel readout technique has been developed for a position-sensitive photomultiplier with a crossed-wire anode. A new charge-sensitive shift register has been used to record the charge collected by each of the anode wires. The performance of a position-sensitive scintillation counter as a function of photon energy and position has been studied using this new technique. A variety of algorithms for reconstructing the energy and position of each event using the individual anode signals are discussed and the potential benefits of this more complex readout system will be illustrated. Compared with the traditional centroiding technique, the individual anode readout method promises better spatial linearity over the entire photomultiplier sensitive area as well as a significant reduction in the low energy threshold.