In microeconometric applications, simulation methods such as the Method of Simulated Moments (MSM) and Indirect Inference (II) typically provide consistent and asymptotically normal estimators when a finite number of simulation draws per observation is used. However, these estimators are inefficient, unless the number of simulation draws per observation is large (theoretically, infinite). This paper argues that this inefficiency can be attributed to the standard estimators ignoring important information about the estimation problem. The paper proves that asymptotically efficient estimation is possible with as little as one simulation draw per observation, as long as the estimators make proper use of the available information. Moreover, such efficient estimators can be taken to be simple modifications of the standard MSM and II estimators with nearly no additional computational or programming burden. In practice, the possibility of using just one simulation draw per observation could significantly reduce the estimation time for models, in which evaluation at each simulation draw and parameter value is time-consuming. This in particular includes models that require numerical computation of an optimal choice, decision, or equilibrium for each simulation draw. Such models are widespread in empirical microeconomics, including industrial organization and labor economics. To establish the properties of the new estimators, the paper develops an asymptotic theory of estimation and inference in (possibly non-smooth) moment condition models with a large number of moments. This asymptotic theory covers both the extremum and quasi-Bayesian estimators.