An evidence game is a strategic disclosure game in which an agent who has different pieces of verifiable evidence decides which ones to disclose and which ones to conceal, and a principal chooses an action (a "reward"). The agent's preference is the same regardless of his information (his "type")—he always prefers the reward to be as high as possible—whereas the principal prefers the reward to fit the agent's type. We compare the setup where the principal chooses the action only after seeing the disclosed evidence, to the setup where the principal can commit ahead of time to a reward policy (the latter is the standard mechanism-design setup). We compare the setup where the principal chooses the action only after seeing the disclosed evidence to the setup where the principal can commit ahead of time to a reward policy (the mechanism-design setup). The main result is that under natural conditions on the truth structure of the evidence, the two setups yield the same equilibrium outcome.