Low-noise noise generally refers to narrow-band noise with a flat temporal envelope. Hartmann and Pumplin [J. Acoust. Soc. Am. 83, 2277--2289 (1988)] used one 100-Hz-wide low-noise noise sample to mask a sinusoidal signal, and found that thresholds were 5 dB lower than for a comparable Gaussian noise. These experiments were performed as frozen-noise measurements and the threshold values were the averages of the results for six different signal starting phases. The thresholds for the signal in Gaussian noise (about -11-dB signal-to-overall-noise ratio) were considerably lower than thresholds typically found in a random-noise presentation (-3 dB). The experiments reported here were initiated to test whether the difference in masking behavior between low-noise noise and Gaussian noise is also observed in a random-noise experiment and how it depends on masker bandwidth and signal duration. In a 100-Hz-wide masker centered at 1000 Hz, the same difference of about 5 dB was found. This difference increases with decreasing masker bandwidth, reaching a maximum of 9.5 dB for a 10-Hz-wide masker. The difference also increases somewhat with decreasing signal duration, from 5 dB for a 500-ms signal to 7.6 dB for a 20-ms signal.