Detection and lateralization performance were measured using as a signal the same narrow band of noise that served as the masker. The center frequency of the noise band was either 1000 or 2000 Hz, in different experiments. Both diotic (N0‐S0) and dichotic (N0‐Sπ) data were taken at both frequencies. By varying the signal‐to‐masker ratio and the angle α at which the signal is added to the masker in the N0‐Sπ condition, it is possible to control the magnitudes of the two binaural cues—interaural time difference and interaural level difference. The outcomes at 1000 Hz support our previous findings—subjects differ in their sensitivities to the two cues, and the cues do not cancel perfectly when the task is detection. At 2000 Hz, even relatively large interaural time differences were of little or no benefit either for detection or lateralization, and interaural level difference was the primary binaural cue. At 1000 Hz, sizeable masking‐level differences (MLDs) were observed for all subjects at all values of α. At 2000 Hz, the MLDs were large at α = 0°; however, detectability was essentially the same in the conditions N0‐Sπ, α = 90°, and N0‐S0, α = 90° implying that in both of these conditions performance was based on the increment in level that occurred with signal onset.