Global stressors, including climate change, are a major threat to ecosystems, but they cannot be halted by local actions. Ecosystem management is thus attempting to compensate for the impacts of global stressors by reducing local stressors, such as overfishing. This approach assumes that stressors interact additively or synergistically, whereby the combined effect of two stressors is at least the sum of their isolated effects. It is not clear, however, how management should proceed for antagonistic interactions among stressors, where multiple stressors do not have an additive or greater impact. Research to date has focussed on identifying synergisms among stressors, but antagonisms may be just as common. We examined the effectiveness of management when faced with different types of interactions in two systems--seagrass and fish communities--where the global stressor was climate change but the local stressors were different. When there were synergisms, mitigating local stressors delivered greater gains, whereas when there were antagonisms, management of local stressors was ineffective or even degraded ecosystems. These results suggest that reducing a local stressor can compensate for climate change impacts if there is a synergistic interaction. Conversely, if there is an antagonistic interaction, management of local stressors will have the greatest benefits in areas of refuge from climate change. A balanced research agenda, investigating both antagonistic and synergistic interaction types, is needed to inform management priorities.