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Traditionally, studies of intrasexual selection have focused on single traits that are more exaggerated in males. Relatively little is known about systems in which traits are larger in females or the role of multiple traits in male contests. We used a tournament design in which each male encounters a series of different opponents, in conjunction with the structured Bradley–Terry model, to examine the role of multiple male traits in contests between male Cape dwarf chameleons, Bradypodion pumilum. Females are larger but males have relatively longer tails, larger and more ornamented heads and a larger central flank patch, all of which are emphasized during agonistic displays. We found no evidence that larger body size confers an advantage in male contests, despite high levels of aggression and escalated encounters. However, both the height of the casque (head ornament) and relative area of the flank patch were …