We ask how far the choice of which moments to match can push estimates in misspecified structural models. The answer is: very far. Under regularity conditions, an adversarial researcher informed about the data distribution can choose moments that render any parameter value the unique solution to the population moment-matching problem. Moreover, in many cases they can do so with little increase in model-implied standard errors relative to maximum likelihood. We illustrate both results in a menu-cost model.<br><br>Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at <a href="http://www.nber.org/papers/&#119;35378" TARGET="_blank">www.nber.org</a>.<br>