We explore the statistical properties of natural sound stimuli pre-processed with a bank of linear filters. The responses of such filters exhibit a striking form of statistical dependency, in which the response variance of each filter grows with the response amplitude of filters tuned for nearby frequencies. These dependencies may be substantially reduced using an operation known as divisive normalization, in which the response of each filter is divided by a weighted sum of the rectified responses of other filters. The weights may be chosen to maximize the independence of the normalized responses for an ensemble of natural sounds. We demonstrate that the resulting model accounts for non-linearities in the response characteristics of the auditory nerve, by comparing model simulations to electrophysiological recordings. In previous work (NIPS, 1998) we demonstrated that an analogous model derived from the statistics of natural images accounts for non-linear properties of neurons in primary visual cortex. Thus, divisive normalization appears to be a generic mechanism for eliminating a type of statistical dependency that is prevalent in natural signals of different modalities.