Resolving conflicting ecosystem management goals - such as maintaining fisheries while conserving marine species or harvesting timber while preserving habitat - is a widely recognized challenge. Even more challenging may be conflicts between two conservation goals that are typically considered complementary. Here, we model a case where eradication of an invasive plant, hybrid Spartina, threatens the recovery of an endangered bird that uses Spartina for nesting. Achieving both goals requires restoration of native Spartina. We show that the optimal management entails less intensive treatment over longer time scales to fit with the time scale of natural processes. In contrast, both eradication and restoration, when considered separately, would optimally proceed as fast as possible. Thus, managers should simultaneously consider multiple, potentially conflicting goals, which may require flexibility in the timing of expenditures.