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