The effects of masker bandwidth on the detection of narrow‐ and wideband signals have been investigated. For both kinds of signals, plots of threshold as a function of masker bandwidth yielded by both narrow‐ and wideband signals are reasonably described with two intersecting lines. Thresholds initially increase with masker bandwidth and then become independent of further increases. The rate of increase depends on the signal spectrum. The bandwidth at which the lines intersect varies with signal bandwidth and also mode of masker presentation (i.e., whether the masker is gated with the signal or is present continuously). Internal filtering is most accurate when the masker is present continuously. A model is proposed in which a listener’s decisions about the presence of narrow‐band signals are based upon estimates of stimulus energy within a critical band. These estimates are degraded by bandwidth‐dependent processing errors. When the signal to be detected spans several critical bands (i.e., is wideband), the model forms a test statistic by summing the outputs of the relevant critical bands. The model permits the contribution of each band to the sum to vary with masker bandwidth because it incorporates a form of lateral suppression. Thresholds of narrow‐band signals in gated maskers and wideband signals in gated and continuous maskers are predicted by the model. However, the model fails to account for the detectability of narrow‐band signals in continuous maskers.