Reef-building corals, like many long-lived organisms, experience environmental change as a combination of separate but concurrent processes, some of which are gradual yet long-lasting, while others are more acute but short-lived. For corals, some chronic environmental stressors, such as rising temperature and ocean acidification, are thought to induce gradual changes in colonies’ vital rates. Meanwhile, other environmental changes, such as the intensification of tropical cyclones, change the disturbance regime that corals experience. Here, we use a physiologically structured population model to explore how chronic environmental stressors that impact the vital rates of individual coral colonies interact with the intensity and magnitude of disturbance to affect coral population dynamics and cover. We find that, when disturbances are relatively benign, intraspecific density dependence driven by space competition partially buffers coral populations against gradual changes in vital rates. However, the impact of chronic stressors is amplified in more highly disturbed environments, because disturbance weakens the buffering effect of space competition. We also show that coral cover is more sensitive to changes in colony growth and mortality than to external recruitment, at least in open populations, and that space competition and size structure mediate the extent and pace of coral population recovery following a large-scale mortality event. Understanding the complex interplay among chronic environmental stressors, mass-mortality events, and population size structure sharpens our ability to manage and to restore coral-reef ecosystems in an increasingly disturbed future.