In vision of everyday scenes, features requiring detection are frequently observed in the presence of suprathreshold background structures. Detection of such features is a contrast discrimination task and is often necessary for the subsequent process of recognition. In order to provide a description of this task, contrast discrimination measurements were determined for targets having luminance profiles which were localised in both space and spatial frequency. The investigation extends earlier work on this topic by measurement of contrast discrimination levels for different base contrasts, sizes,, luminances and aspect ratios of the targets. For all conditions, it is shown that the functional variation of the contrast discrimination level with base contrast can be described, approximately, by a single curve with one scaling constant. This constant is specified by the contrast threshold level of the target. A model is proposed to describe the contrast discrimination process. The model contains two noise sources, one with noise level proportional to the target contrast and the other with noise level proportional to the contrast thershold level of the target. Predictions from the model adequately describe the experimental data of contrast discrimination against base contrast and, in addition, fit data on the probability of discrimination against the level of contrast difference. An example is given of a simple application of the model to the determination of the number of discriminable steps in contrast as a function of the spatial frequency of a sinusoidal grating target.