Interaural level differences (ILDs) provide salient cues for localizing high frequency sounds in space, and populations of neurons that are sensitive to ILDs are found at almost every synaptic level from brainstem to cortex. These cells are predominantly excited by stimulation of one ear and predominantly inhibited by stimulation of the other ear, such that the magnitude of their response is determined in large part by the intensities at the two ears. However, in many cases ILD sensitivity is also influenced by overall intensity, which challenges the idea of unambiguous ILD coding. We investigated whether ambiguity is reduced from one synaptic level to another for two centers in the so-called ILD processing pathway. We recorded from single cells in the free-tailed bat lateral superior olive (LSO), the first station where ILDs are coded, and the central nucleus of the inferior colliculus (ICC), which receives a strong projection from the LSO, as well as convergent projections from many other auditory centers. We assessed effects of overall intensity by comparing ILD functions generated with different fixed intensities to the excitatory ear. LSO cells were characterized by functions that shifted in a systematic manner with increasing intensity to the excitatory ear. In contrast, significantly more ICC cells had functions that were stable across overall sound intensity, indicating that hierarchical transformations increase stability. Furthermore, a population analyses based on proportion of active cells indicated that stability in the ICC was greatly enhanced when overall population activity was considered.