A narrow band of noise (50 Hz wide centered at 250 Hz) was passed through a phase‐shifting network and was then used as both masker and signal. The phase shifter permitted control over the phase angle α at which the signal and the masker were added. The masker was continuously present and was in‐phase interaurally N0); the signal could be presented in‐phase interaurally (S0) or 180° out‐of‐phase (Sπ). Detection data were taken for N0‐S0, α = 0° (increments) and α = 180° (decrements), and both detection and lateralization data were taken for N0‐Sπ for several values of α. A single‐interval psychophysical method was used throughout. For all subjects for all values of α, the masking‐level differences (MLDs) were positive and substantial. In the N0‐Sπ conditions, two cues were available to the subject for all values of α except 0° and 90°—an interaural phase (time) difference and an interaural difference in level. Between α = 0° and α = 90 °, the two cues are consonant, but between α = 90° and α = 180°, the two cues are in opposition, i.e., one cue indicates that the sound source is to one side of the median plane while the other cue indicates that it is to the other side. Some subjects were more sensitive to one of these cues, and other subjects were more sensitive to the other cue; this fact was apparent in both their detection and their lateralization data. For each subject there was a value of α between about 120° and 170° at which detection performance was good while lateralization was nearly impossible.