We propose a method for identifying a set of colours for displaying 2D and 3D categorical images when the categories are unordered labels. The principle is to find maximally distinct sets of colours. We either generate colours sequentially, to maximize the dissimilarity or distance between a new colour and the set of colours already chosen, or use a simulated annealing algorithm to find a set of colours of specified size. In both cases, we use a Euclidean metric on the perceptual colour space, CIELAB, to specify distances. (c) 2007 Wiley Periodicals, Inc. Col Res Appl, 32, 304-309, 2007.