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We consider an agent that operates with two models of the environment: one that captures expected behaviors and one that captures additional exceptional behaviors. We study the problem of synthesizing agent strategies that enforce a goal against environments operating as expected while also making a best effort against exceptional environment behaviors. We formalize these concepts in the context of linear-temporal logic, and give an algorithm for solving this problem. We also show that there is no trade-off between enforcing the goal under the expected environment specification and making a best-effort for it under the exceptional one.