Major nuclei of the superior olivary complex--the lateral superior olive (LSO) and the medial superior olive (MSO) are presumed to play a major role in the localization of sound signals using interaural level and interaural phase differences between the signals arriving at the two ears. The present work develops a novel approach--function based modeling--for assessing the role of these nuclei in binaural localization. The interaural level difference is shown to be the sufficient statistic at high frequencies when only level cues are available. This level difference is processed optimally when the inputs are excitatory from one ear and inhibitory from the other ear. Response characteristics of LSO single units are remarkably similar to the optimal processor's, strongly supporting the notion that LSO units are intimately involved in high-frequency binaural hearing. For low frequencies the optimal processor makes use of the interaural phase difference cue by correlating the inputs to the two ears thus requiring that the two inputs be excitatory. Hence, high and low frequency localization systems are shown to differ greatly, suggesting separate pathways for each.