A classic problem in coexistence theory is how grasses and trees coexist in savannas. A popular deterministic model of savannas, the rooting niche separation model, is based on an assumption that is not empirically supported in many savannas. Alternative models that do not rely on the rooting niche assumption invoke intricate stochastic mechanisms that limit their attractiveness as general models of savannas. In this article we develop an alternative deterministic model of grass-tree interactions and use it to analyze the conditions under which grass-tree coexistence is possible. The novel feature of this model is that it partitions aboveground and belowground competition and simulates the fact that fire and herbivory remove only aboveground biomass. The model predicts that stable coexistence of grasses and trees is possible, even when grasses and trees do not have separate rooting niches. We show that when aboveground competition is intense, grasses can be excluded by trees; under such conditions, fire can prevent grasses from exclusion and induce a stable savanna state. The model provides a general framework for exploring the interactive effects of competition, herbivory, and fire on savanna systems.