Two nonlinear modeling methods were used to characterize the input/output relationships of type IV units, which are one principal cell type in the dorsal cochlear nucleus (DCN). In both cases, the goal was to derive predictive models, i.e., models that could predict the responses to other stimuli. In one method, frequency integration was estimated from response maps derived from single tones and simultaneous pairs of tones presented over a range of frequencies. This model combined linear integration of energy across frequency and nonlinear interactions of energy at different frequencies. The model was used to predict responses to noisebands with varying width and center frequency. In almost all cases, predictions using two-tone interactions were better than linear predictions based on single-tone responses only. In about half the cases, reasonable quantitative fits were achieved. The fits were best for noisebands with narrow bandwidth and low sound levels. In the second nonlinear method, the spectrotemporal receptive field (STRF) was derived from responses to broadband stimuli. The STRF could account for some qualitative features of the responses to broad noisebands and spectral notches embedded in broad noisebands. Quantitatively, however, the STRFs failed to predict the responses of type IV units even to simple broadband noise stimuli. For narrowband stimuli, the STRF failed to predict even qualitative features (such as excitatory and inhibitory frequency bands). The responses of DCN type IV units presumably result from interactions of two inhibitory sources, a strong one that is preferentially activated by narrowband stimuli and a weaker one that is preferentially activated by broadband stimuli. The results presented here suggest that the STRF measures effects related to the broadband inhibition, whereas two-tone interactions measure mostly effects related to narrowband inhibition. This explains why models based on two-tone interactions predict the responses to narrow noisebands much better then models based on STRFs. It is concluded that a minimal stimulus set for characterizing type IV units must contain both broadband and narrowband stimuli, because each stimulus class by itself activates only partially the integration mechanisms that shape the responses of type IV units. Similar conclusions are expected to hold in other parts of the auditory system: when characterizing a complex auditory unit, it is necessary to use a range of stimuli to ensure that all integration mechanisms are activated.