Thresholds for binaurally in-phase (SO) and out-of-phase (Sπ) tones masked by diotic noise were measured as a function of noise bandwidth at 250 and 4000 Hz. Results show that the familiar dependence of the MLD for a tone in wideband noise on the frequency of the tone derives primarily from the dependence of critical bandwidth on frequency and only secondarily from a frequency dependence, per se. MLD's measured with narrowband (≈10 Hz) noise muskets are 25–30 dB at 250 Hz and about 20 dB at 4000 Hz. The difference between Sπ thresholds at 250 Hz and 4 kHz measured with narrowband maskers supports the hypothesis that the detection cue is interaural phase difference at low frequencies and interaural amplitude difference at high frequencies. In both frequency regions, “binaural sluggishness,” which has been documented by Grantham and Wightman [J. Acoust. Soc. Am. 63, 511–523 (1978)], is evident in the increase of the Sπ threshold with an increase in noise bandwidth at narrow bandwidths. [Work supported by NIH.]