Savanna tree species vary in the magnitude of their response to grass competition, but the functional traits that explain this variation remain largely unknown. To address this gap, we grew seedlings of 10 savanna tree species with and without grasses in a controlled greenhouse experiment. We found strong interspecific differences in tree competitive response, which was positively related to photosynthesis rates, suggesting a trade-off between the ability to grow well under conditions of low and high grass biomass across tree species. We also found no competitive effect of tree seedlings on grass, suggesting strong tree-grass competitive asymmetry. Our results identify a potentially important trade-off that enhances our ability to predict how savanna tree communities might respond to variation in grass competition.