Neurons in the dorsal cochlear nucleus (DCN) exhibit nonlinearities in spectral processing, which make it difficult to predict the neurons’ responses to stimuli. Here, we consider two possible sources of nonlinearity: non-monotonic responses as sound level increases due to inhibition; and interactions between frequency components. A spectral weighting function model of rate responses is used; the model approximates the neuron’s rate response as a weighted sum of the frequency components of the stimulus plus a 2nd-order sum that captures interactions between frequencies. Such models approximate DCN neurons well at low spectral contrast, i.e. when the standard deviation (contrast) of the stimulus spectrum is limited to 3 dB. This model is compared to a 1st-order sum with weights that are explicit functions of sound level, so that the low contrast model is extended to spectral contrasts of 12 dB, the range of natural stimuli. The sound-level dependent weights improve prediction performance at large spectral contrast. However, the interactions between frequencies, represented as 2nd-order terms, are more important at low spectral contrast. The level-dependent model is shown to predict previously described patterns of responses to spectral edges, showing that small changes in the inhibitory components of the receptive field can produce large changes in the responses of the neuron to features of natural stimuli. These results provide an effective way of characterizing nonlinear auditory neurons incorporating stimulus-dependent sensitivity changes. Such models could be used for neurons in other sensory systems, which show similar effects.