While optimally weighted GMM estimation has desirable large sample properties, its small sample performance is poor in some applications. We propose a computationally simple alternative, for weakly dependent data generating mechanisms, based on minimization of the Kullback-Leibler Information Criterion. Conditions are derived under which the large sample properties of this estimator are similar to GMM, i.e., the estimator will be consistent and asymptotically normal, with the same asymptotic covariance matrix as GMM. In addition, we propose overidentifying and parametric restrictions tests as alternatives to analogous GMM procedures.