This paper explores how different high-dimensional feature spaces might be represented in cortical maps, subject to continuity and completeness constraints. Spaces explored included products of circular variables (such as orientation), products of linear dimensions encoding scalar features (such as spatial frequency) and products of binary features. Maps were generated using the Kohonen algorithm, with uniform or non-uniform stimulus distributions. A 2D retina was always assumed to be present. Simulations were run with and without annealing. For uniform input distributions, coverage uniformity (Swindale 1991 Biol. Cybern. 65 415-24) was used to measure how well the map was able to represent the feature space. For non-uniform distributions a weighted measure of coverage uniformity was calculated. Good coverage could be achieved for up to five or six cyclic variables but was substantially worse for a similar number of uniformly distributed scalar features. For annealed maps of multi-dimensional stimuli with Gaussian distributions, the distribution of receptive field centres and the distribution of total activity evoked on the cortex matched the stimulus distribution well. For annealed maps of non-uniformly distributed binary features there was an approximately linear relationship between the area of a map devoted to a specific feature and the probability of occurrence of the feature during development. Deviations from uniform retinotopy often led to improved coverage.