Statistical analysis of natural sounds and speech reveals logarithmically distributed spectrotemporal modulations that can cover several orders of magnitude. By contrast, most artificial stimuli used to probe auditory function, including pure tones and white noise, have linearly distributed amplitude fluctuations with a limited average dynamic range. Here we explore whether the operating range of the auditory system is physically matched to the statistical structure of natural sounds. We recorded single-unit and multi-unit neuronal activity from the central nucleus of the cat inferior colliculus (ICC) in response to dynamic spectrotemporal sound sequences to determine whether ICC neurons respond preferentially to linear or logarithmic spectrotemporal amplitudes. We varied the intensity, dynamic range, and contrast statistics of these sounds to mimic those of natural and artificial stimuli. ICC neurons exhibited monotonic and nonmonotonic contrast dependencies with increasing dynamic range that were independent of the stimulus intensity. Midbrain neurons had higher firing rates and higher receptive field energies and showed a net improvement in spectrotemporal encoding ability for logarithmic stimuli, with an increase in the mutual information rate of approximately 50% over linear amplitude sounds. This efficient use of logarithmic spectrotemporal modulations by auditory midbrain neurons reflects a neural adaptation to structural regularities in natural sounds and likely underlies human perceptual abilities.