Competition involves two dimensions, rivalry for resources and social-status ranking. In our experiment we exclude the first dimension and investigate gender differences in the preference for status ranking. Participants perform a task under non-rivalry incentives. Before doing so, individuals indicate whether they prefer to do the task in an environment with social-status ranking or one without, knowing whether the ranking will be done by a man or a woman. We find no gender difference in status-ranking aversion when the ranker is a woman. When ranked by a man, women’s preference for status ranking is the same as with a female ranker, whereas that of men increases. As a consequence, with a male ranker, women’s preference for status ranking is lower than that of men. This finding complements the established result that women are averse to competing under rivalry for resources and points to an effect that goes beyond it. In the social-status ranking of competition, the gender difference is only observed when the ranking is done by a man. For the rivalry dimension, the impact on the behavior of male and female decision-makers may therefore also depend on the gender of those organizing, supervising and witnessing the competition.