Adaptation to stimulus statistics, such as the mean level and contrast of recently heard sounds, has been demonstrated at various levels of theauditory pathway. It allows the nervous system to operate over the wide range of intensities and contrasts found in the natural world. Yet current standard models of the response properties of auditory neurons do not incorporate such adaptation. Here we present a model of neural responses in the ferret auditory cortex (the IC Adaptation model), which takes into account adaptation to mean sound level at a lower level of processing: the inferior colliculus (IC). The model performs high-pass filtering with frequency-dependent time constants on the sound spectrogram, followed by half-wave rectification, and passes the output to a standard linear-nonlinear (LN) model. We find that the IC Adaptation model consistently predictscortical responses better than the standard LN model for a range of synthetic and natural stimuli. The IC Adaptation model introduces no extra free parameters, so it improves predictions without sacrificing parsimony. Furthermore, the time constants of adaptation in the IC appear to be matched to the statistics of natural sounds, suggesting that neurons in the auditory midbrain predict the mean level of future sounds and adapt their responses appropriately.