Resource competition theory predicts coexistence and exclusion patterns based on species’ R*s, the minimum resource values required for a species to persist. A central assumption of the theory is that all species have equal access to resources. However, many systems are characterized by preemption exploitation, where some species deplete resources before their competitors can access them (e.g., asymmetric light competition, contest competition among animals). We hypothesized that coexistence under preemption requires an R*-preemption trade-off—that is, the species with the priority access should have a higher R* (lower “efficiency”). Thus, we developed an extension of resource competition theory to investigate partial and total preemption (in the latter, the preemptor is unaffected by species with lower preemption rank). We found that an R*-preemption trade-off is a necessary condition for coexistence in all models. Moreover, under total preemption, the trade-off alone is sufficient for coexistence. In contrast, under partial preemption, more conditions are needed, which restricts the parameter space of coexistence. Finally, we discuss the implications of our finding for seemingly distinct trade-offs, which we view as special cases of the R*-preemption trade-off. These trade-offs include the digger-grazer trade-off, the competition-colonization trade-off, and trade-offs related to light competition between trees and understories.