The results of previous “time‐intensity tradability” experiments and binaural detection experiments using phase‐coherent targets and maskers have indicated that other attributes of a low‐frequency binaural tone besides pitch, loudness, and the laterality of its dominant spatial image are available as cues in interaural discrimination experiments. These results are compared to predictions of simple models based on optimal processing of two partially correlated Gaussian decision variables derived from the interaural time and intensity differences of tonal stimuli. Models in which one decision variable is proportional to time delay and the other to intensity difference fail to describe the experimental data. However, the predictions of a model using one decision variable related to the laterality of a time‐intensity‐traded image and a second variable proportional to either the interaural time or intensity difference alone are in reasonable agreement with the experimental results. Individual differences across subjects and experiments were found in model parameters related to the correlation of the two decision variables and the time‐intensity trading ratio that most closely fit the data. [Supported by NIH.]