In this study, we explored ways to account more accurately for responses of neurons in primary auditory cortex (A1) to natural sounds. The auditory cortex has evolved to extract behaviorally relevant information from complex natural sounds, but most of our understanding of its function is derived from experiments using simple synthetic stimuli. Previous neurophysiological studies have found that existing models, such as the linear spectro-temporal receptive field (STRF), fail to capture the entire functional relationship between natural stimuli and neural responses. To study this problem, we compared STRFs for A1 neurons estimated using a natural stimulus, continuous speech, with STRFs estimated using synthetic ripple noise. For about one-third of the neurons, we found significant differences between STRFs, usually in the temporal dynamics of inhibition and/or overall gain. This shift in tuning resulted primarily from differences in the coarse temporal structure of the speech and noise stimuli. Using simulations, we found that the stimulus dependence of spectro-temporal tuning can be explained by a model in which synaptic inputs to A1 neurons are susceptible to rapid nonlinear depression. This dynamic reshaping of spectro-temporal tuning suggests that synaptic depression may enable efficient encoding of natural auditory stimuli.