Thresholds for the detection of 500‐ms tones in noise at either 0.25 or 4 kHz and either interaurally in‐phase (NoSo) or out‐of‐phase (NoSπ) were measured as a function of the bandwidth of a diotic masking noise (with total noise power held constant). NoSo thresholds followed the classic trend indicative of an effective critical band in noise masking. NoSπ thresholds also indicated critical‐band filtering, but with a wider effective critical bandwidth. At subcritical masker bandwidths, for both 0.25 and 4 kHz, NoSπ thresholds increased with an increase in noise bandwidth, despite the fact that total noise power was constant. This latter finding is attributed to binaural insensitivity to rapid fluctuations in the interaural cues that subserve detection in the NoSπ condition. These results suggest a new interpretation for the small difference between NoSo and NoSπ thresholds measured with high‐frequency tones in a broadband noise masker. This interpretation is based partly on the inability to utilize rapidly varying interaural cues, partly on out‐of‐band interference effects, and partly on loss of information related to stimulus fine structure.