Generalized method of moments and continuous updating estimators based on second- to fourth-order moment conditions can be used to solve the identification problem and estimate non-Gaussian structural vectorautoregressions. However, estimating the asymptotically optimal weighting matrix and the asymptotic variance of the estimators is challenging in small samples. I show that this can lead to a severe bias, large variance, and inaccurate inference in small samples. I propose to use the assumption of independent structural shocks not only to derive moment conditions but also to derive alternative estimators for the asymptotically optimal weighting matrix and the asymptotic variance of the estimator. I demonstrate that these estimators greatly improve the performance of the generalized method of moments and continuous updating estimators in terms of bias, variance, and inference.