A wide range of econometric and statistical models are specified through
moment conditions. Efficient estimation of such models essentially employs two distinct ideas: optimally combining estimation equations (e.g., the optimal estimating equations of Godambe (1976), the generalized method of moments of Hansen (1982) and the empirical likelihood of Qin and Lawless (1994)), and optimally combining estimators (e.g., the weighted method of moments of Xiao (2010)). This paper extends these methods to moment condition models with heterogeneous populations. Comparison of the finite sample performance of the proposed estimators is conducted through Monte Carlo simulations.