Although most analyses of sexual dimorphism focus on overall body size (sexual size dimorphism), males and females of the same species may differ profoundly in their morphology, performance and behaviour even if the two sexes attain similar adult sizes. Thus, similarity in size may mask major sex-based divergences in traits such as musculature and fat stores. Although female Colombian rainbow boas Epicrates cenchria maurus are slightly longer than males, we show that males are more muscular than females and, accordingly, males outperform same-sized females in tests of strength. Musculature may enhance success in male–male combat. The two sexes also differ in body shape: the wider abdomens of females may allow more space to store fat and/or embryos. Lastly, male boas reacted more overtly to handling (via defecation and striking) than did females. These sex differences in morphology, performance and behaviour plausibly reflect ecological differences between the sexes in the wild, with males under sexual selection for increased physical strength and females under fecundity selection for enhanced reproductive output.