The Weights-Adjusted Second-Order Blind Identification (WASOBI) algorithm was recently proposed (Yeredor, 2000) as an optimized version of the SOBI Algorithm (Belouchrani et al., 1997) for blind separation of static mixtures of Gaussian Moving Average (MA) sources. The optimization consists of transforming the approximate joint diagonalization in SOBI into a properly weighted Least-Squares problem, with the asymptotically optimal weights specified in terms of the estimated correlations. However, only correlations up to the lag of the maximal MA order were used. Somewhat counter-intuitively, it turns out that estimated correlation matrices beyond this lag are also useful, although the respective true correlations are known to be zero and have no direct dependence on the mixing matrix. Nevertheless, when properly incorporated into the weighted least-squares problem, these estimated matrices can significantly improve performance, since they bear information on the estimation errors of the shorter-lags matrices. In this paper we show how to modify the WASOBI algorithm accordingly, and demonstrate the improvement via analysis and simulation results.