The baseline approach for optimal path finding in 4-connected grids is A* with Manhattan Distance. Nevertheless, a large number of enhancements were suggested over the years, usually requiring a preprocessing phase and/or additional memory to store smart lookup tables. In this paper we introduce an enhancement to A* (called BOXA*) on grids which does not need any preprocessing and only needs negligible additional memory. The main idea is to treat the closed-list as a dynamic obstacle. We maintain a list of rectangles which surround CLOSED nodes and calculate an admissible heuristic using the fact that an optimal path from a given node must go around these rectangles. We experimentally show the benefits of this approach on a variety of grid domains.