We define and investigate a property of mechanisms that we call “strategic simplicity,” and that is meant to capture the idea that, in strategically simple mechanisms, strategic choices are easy. We define a mechanism to be strategically simple if strategic choices can be based on first-order beliefs about the other agents’ preferences alone, and there is no need for agents to form higher-order beliefs, because such beliefs are irrelevant to agents’ optimal choices. All dominant strategy mechanisms are strategically simple. But many more mechanisms are strategically simple. In particular, strategically simple mechanisms may be more flexible than dominant strategy mechanisms in the voting problem and the bilateral trade problem..