It is often assumed that listeners detect an increment in the intensity of a pure tone by detecting an increase in the energy falling within the critical band centered on the signal frequency. A noise masker can be used to limit the use of signal energy falling outside of the critical band, but facets of the noise may impact increment detection beyond this intended purpose. The current study evaluated the impact of envelope fluctuation in a noise masker on thresholds for detection of an increment. Thresholds were obtained for detection of an increment in the intensity of a 0.25- or 4-kHz pedestal in quiet and in the presence of noise of varying bandwidth. Results indicate that thresholds for detection of an increment in the intensity of a pure tone increase with increasing bandwidth for an on-frequency noise masker, but are unchanged by an off-frequency noise masker. Neither a model that includes a modulation-filter-bank analysis of envelope modulation nor a model based on discrimination of spectral patterns can account for all aspects of the observed data.