Cells in the lateral superior olive (LSO) are known to be sensitive to interaural intensity differences (IIDs) in that they are excited by IIDs that favor the ipsilateral ear and inhibited by IIDs that favor the contralateral ear. For each LSO neuron there is a particular IID that causes a complete inhibition of discharges, and the IID of complete inhibition varies from neuron to neuron. This variability in IID sensitivity among LSO neurons is a key factor that allows for the coding of a variety of IIDs among the population of cells. A fundamental question concerning the coding of IIDs is: how does each cell in the LSO derive its particular IID sensitivity? Although there have been a large number of neurophysiological studies on the LSO, this question has received little attention. Indeed, the only reports that have directly addressed this question are those of Reed and Blum, who modeled the binaural properties of LSO neurons and proposed that the IID at which discharges are completely suppressed should correspond to the difference in threshold between the excitatory, ipsilateral and inhibitory, contralateral inputs that innervate each LSO cell. The main purpose of this study was to test the threshold difference hypothesis proposed by Reed and Blum by recording responses to monaural stimulation and to IIDs from single cells in the LSO of the mustache bat. Our results show that although the IID sensitivities of some LSO cells correspond to the difference in threshold between the excitatory and inhibitory ears, in the majority of cells the difference in thresholds did not correspond to the cell's IID sensitivity. The results lead us to propose two models to account for IID sensitivities. One model is similar to that proposed by Reed and Blum and emphasizes differences in the thresholds of the excitatory and inhibitory inputs. This model accounts for the minority of cells in which the IID of complete inhibition corresponded to the difference in threshold of the inputs from the two ears. The other model, which accounts for the cells in which the IID of complete inhibition did not correspond to the difference in the thresholds of the inputs from the two ears (the majority of cells), places emphasis on differences in latencies of the excitatory and inhibitory inputs. The models incorporate features that are concordant with the known properties of the neurons that project to the LSO and together can account for the diversity of IID sensitivities among the population of LSO neurons.