We explore variation in the prices paid by recreational hunters of trophy animals in Africa and its possible causes, including perceived rarity. Previous work has raised the possibility that extinction can result if demand rises fast enough as a species becomes rarer. We attempt to disentangle this from other inter-correlated influences affecting price. Species with larger body sizes and larger trophies were more valuable. Value increased less steeply as a function of size for bovids than for felids and the effect was consistent across countries. Power laws, ubiquitous in physical and social systems, described the trends. The exponent was approximately 0.4 for bovids, compared with approximately 1.0 for felids. Rarity (as indexed by IUCN score) influenced the value of bovid trophies - price was higher for species in categories denoting higher global threat. There was substantial variation in price among and within families not explained by either size or rarity. This may be attributable to a 'charisma' effect, which seems likely to be a general attribute of human perceptions of wildlife. Species where prices were higher than predicted by size or rarity are ranked high in published accounts of desirability by hunters. We conclude that the valuation of these species is explicable to a large extent by body size and perceived rarity, and that differences in valuation between taxonomic groups are related to less easily quantified 'charisma' effects. These findings are relevant for conservationists considering the threat status of species exploited in open access markets, and where license quotas are adjusted in response to changes in perceived rarity.