The study of interactions between consumers and their resources has led to three important but largely separate bodies of theory: optimal foraging theory, density-dependent habitat selection, and consumer-resource theory. In this article, we draw on all three to study mechanisms of coexistence, uniting these fields of theory via a set of related models based on Holling's disc equation and four ... [Show full abstract] different types and arrangements of resources. Using established rules for optimal behavior and habitat selection within a framework of consumer-resource models, we explore how unavoidable trade-offs in conversion efficiency, handling time, and encounter efficiency affect coexistence between species. When resources are nutritionally substitutable and spatially mixed, our model predicts that only trade-offs in encounter efficiency can promote coexistence. For spatially separate substitutable resources, any trade-off in encounter, conversion, or handling efficiency allows coexistence. For essential resources, whether mixed or separate, only trade-offs in conversion efficiency can promote coexistence. Since trade-offs that promote coexistence vary depending on the type of resource, this indicates that mechanisms of coexistence can differ depending on how consumers view their resources and how resources are distributed in the environment.