It is now widely recognized that the most commonly used efficient two-step GMM estimator may have large bias in small samples. In this paper we analyze by simulation the finite sample bias of two classes of alternative estimators. The first includes estimators which are asymptotically first-order equivalent to the GMM estimator, namely the continuous-updating, exponential tilting, and empirical likelihood estimators. Analytical and bootstrap bias-adjusted GMM estimators form the second class of alternatives. The Monte Carlo simulation study conducted in the paper for covariance structure models shows that all alternative estimators offer much reduced bias as compared to the GMM estimator, particularly the empirical likelihood and some of the bias-corrected GMM estimators.