The role of sexual selection in shaping the brain is poorly understood. Although numerous studies have investigated the role of natural selection, relatively few have focussed on the role of sexual selection. Two important factors influencing the intensity of sexual selection are sperm competition and pair bonding and three different hypotheses have been proposed to explain how they could influence relative brain size. (1) The ‘extra-pair mating’ hypothesis predicts that sexual dimorphism in brain size will increase with sperm competition intensity. (2) The ‘Machiavellian intelligence’ hypothesis predicts that brain size will be larger in species with intense sperm competition. (3) The ‘relationship intelligence’ hypothesis predicts that species forming long-term pair bonds will have larger brains. We investigated sexual dimorphism in brain size and tested these three hypotheses in waterfowl by studying correlations between relative brain volume and three measures of sperm competition (testicular mass, phallus length and mating strategy) and pair-bond duration using the modern phylogenetic comparative approach. We found no evidence of sexual dimorphism in brain size in waterfowl after controlling for body mass and found no support for any of the three hypotheses. This suggests that brain size may not be sexually selected in waterfowl, despite evidence of sexual selection pressures on other morphological characters.