Bustards vary considerably in sexual size dimorphism (SSD), ranging from reversed-dimorphic species (i.e. male < female) through monornorphic species to species in which an adult male can be three times heavier than an adult female. We used this unusual interspecific variation to test functional hypotheses of SSD using phylogenetic comparative methods. We found a strong allometric relation between SSD and body size that is consistent with Rensch's rule. We then tested whether the intensity of mating competition and the agility of male displays relate to SSD. First, the intensity of mating competition hypothesis predicts that males should be larger than females in species in which the males compete intensely for mates. As predicted, evolutionary changes towards more polygynous mating systems in bustards were associated with relatively larger males. Second, our results are also consistent with the aerial agility hypothesis, since in agile bustards the males tend to be smaller than females, whereas in nonagile bustards the males are usually larger. We also found that these two types of sexual selection have independent and statistically significant influences on SSD. We conclude that SSD in bustards is most consistent with sexual selection, and is influenced by both the intensity of sexual selection and the agility of male displays. Other hypotheses, however, such as fertility selection acting on females and differential use of niches by males and females remain untested. (c) 2006 The Association for the Study of Animal Behaviour Published by Elsevier Ltd. All rights reserved.