Mating systems that comprise a mixture of pure males and self-fertilising hermaphrodites remain an evolutionary enigma. In particular, our understanding of the sexual selection pressures associated with such mating systems is nascent. Males can only reproduce by fertilising hermaphrodites’ eggs, but hermaphrodites can also fertilise their own eggs and gain a genetic advantage by doing so. Consequently, there should be intense competition among males to access hermaphrodites. Here, we test the importance of male size, colour and heterozygosity in predicting the outcome of male–male competition using the mangrove rivulus, which has a male-hermaphrodite mixed-mating system. We pitted males against one another in dyadic laboratory trials to develop a dominance score for each male. We then correlated these scores with male length, several components of male colour, and heterozygosity. Male size was the only significant correlate of dominance: larger males dominated smaller males, implying selection for large male size. However, male mangrove rivulus are similar in size to hermaphrodites, indicating that directional selection for large body size in males is no greater than it is in hermaphrodites. Across all trials, colour was unrelated to dominance, but contests between similarly sized males were usually won by more colourful individuals. As mangrove rivulus are dichromatic, we suspect that male colour may prove to be more important in mate choice than we found it to be in intrasexual competition. Heterozygosity did not explain dominance directly, but correlated strongly with male size, implying an indirect role in intrasexual competition.