The psychophysical task of discriminating changes in the slopes of the amplitude spectra of complex images has been used in the past to test whether the human visual system might be optimised for coding the spatial structure in natural images (e.g. Knill et al., 1990; Tadmor & Tolhurst, 1994). We have reported that the dependency of these discrimination thresholds on the reference slope has the same overall general form, regardless of the particular digitised photographs that are used for generating the stimuli. The actual discrimination thresholds, however, differ markedly in magnitude for stimuli that are derived from different digitised photographs. Here, we describe a model that aims at explaining this diversity of threshold magnitudes: we suppose that the observer is detecting small changes in image contrast estimated within limited spatial-frequency bands of about 1 octave bandwidth. This local-contrast analysis reveals that contrast changes in only one frequency band are of comparable magnitudes to the changes that observers need for detecting differences in the Michelson contrast of simple sinusoidal gratings. The success of this band-limited contrast model is further shown in experiments where the slopes of the amplitude spectra of stimuli were changed only within restricted frequency bands. We show that when the slope is changed outside the limited frequency band implicated by the contrast model, the observer's thresholds are greatly elevated. Thresholds remain unchanged when slope changes are made within the implicated band. We also find that the exact bandwidth of the contrast operator is not critical, provided that it is in the range of about 0.6-1.5, which is the characteristic bandwidth range of V1 neurons.