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In this paper, a new strategy for discrete optimization of a function is presented. Let be the region in the -dimensional parameter space, where is less than some constant. First, is located and characterized by a Gaussian search process, called Gaussian adaptation. This makes it possible to approximate the behavior of . over by a quadratic function . is then optimized for the best discrete solutions using a branch and bound technique. Finally, these points are evaluated for the best points. By various digital filter examples it will be demonstrated that the new method is more capable of finding good solutions than methods presented so far.