Human listeners are sensitive to interaural time differences (ITDs) in the envelopes of sounds, which can serve as a cue for sound localization. Many high-frequency neurons in the mammalian inferior colliculus (IC) are sensitive to envelope-ITDs of sinusoidally amplitude-modulated (SAM) sounds. Typically, envelope-ITD-sensitive IC neurons exhibit either peak-type sensitivity, discharging maximally at the same delay across frequencies, or trough-type sensitivity, discharging minimally at the same delay across frequencies, consistent with responses observed at the primary site of binaural interaction in the medial and lateral superior olives (MSO and LSO), respectively. However, some high-frequency IC neurons exhibit dual types of envelope-ITD sensitivity in their responses to SAM tones, that is, they exhibit peak-type sensitivity at some modulation frequencies and trough-type sensitivity at other frequencies. Here we show that high-frequency IC neurons in the unanesthetized rabbit can also exhibit dual types of envelope-ITD sensitivity in their responses to SAM noise. Such complex responses to SAM stimuli could be achieved by convergent inputs from MSO and LSO onto single IC neurons. We test this hypothesis by implementing a physiologically explicit, computational model of the binaural pathway. Specifically, we examined envelope-ITD sensitivity of a simple model IC neuron that receives convergent inputs from MSO and LSO model neurons. We show that dual envelope-ITD sensitivity emerges in the IC when convergent MSO and LSO inputs are differentially tuned for modulation frequency.