(eng): Inspired by Floating Search, our new pair of methods, the Sequential Forward Retreating Search (SFRS) and Sequential Backward Retreating Search (SBRS) is exceptionally suitable for Wrapper based feature selection. (Conversely, it cannot be used with monotonic criteria.) Unlike most of other known sub-optimal search methods, both the SFRS and SBRS are parameter-free deterministic sequential procedures that incorporate in the optimization process both the search for the best subset and the determination of the best subset size. The subset yielded by either of the two new methods is to be expected closer to optimum than the best of all subsets yielded in one run of the Floating Search. Retreating Search time complexity is to be expected slightly worse but in the same order of magnitude as that of the Floating Search. In addition to introducing the new methods we provide a testing framework to evaluate them with respect to other existing tools.