We present (I) a composite rarity-based iterative reserve selection (CRIRS) algorithm and apply it to three regional mammal databases in north-eastern South Africa. Two types of 'rarity' are used to resolve ties between 25 x 25-km grid cells in the region, species-specific conservation priority scores and conventional database rarity. As expected, grid cell pre-selection (the forced inclusion of grid cells with a specified percentage of their areas dedicated to conservation) and grid cell filtering (the removal of unsuitable grid cells from consideration by the 'near minimum set' (NMS) algorithm) results in decreased efficiency of species representation. Grid cell post-selection, to add the top 5% of richest sites to the selected NMS sites, indicates minimal overlap between rarity-and richness-based procedures. (2) A comparison with the Nicholls and Margules (1993) algorithm (Biol. Con., 64, 165-169) reveals minor differences in efficiency, whereas different input data sets influence the relative efficiencies and extent of grid cell sharing by these algorithms. (3) A further 'greedy' algorithm, which assigns 'relative biodiversity scores' (RES) to sites by combining grid cell richness and summed rarity scores, is presented This enables biodiversity assessments to be incorporated into development planning. These three approaches (CRIRS, Nicholls & Margules (1993) and RBS) and single-criterion variations of the CRIRS algorithm ave compared using mammal data from north-eastern South Africa and their respective strengths are emphasized. (C) 1997 Published by Elsevier Science Ltd.