An efficient method is proposed for the practical solution of the "sign" problem for integrals involved in the semiclassical initial value representation. It is based on a generalization of the conventional Filinov filtering procedure which has the (approximate) effect of incorporating complex initial conditions into the phase space average; it does this by including an explicit oscillatory term in the filtering function that partially cancels the oscillatory part of the original integrand. A systematic procedure is also described for making an optimal choice of the "smoothing parameters," thus removing this arbitrariness in the overall approach. Tests on systems with chaotic dynamics demonstrate the accuracy and efficiency of the method.