This work describes a new best-first bidirectional heuristic search algorithm with two phases. The new algorithm is based on a critical review of the basic search reduction operations in previous algorithms like BS* or Switch-A*. The general guideline is to let search fronts meet as close to midground as possible. In a first phase, search is discontinued at nodes as soon as the opposite frontier is met, terminating when one of the fronts runs out of open nodes. In a second phase, unidirectional search is conducted from the discontinued nodes until an optimal solution can be guaranteed. The new algorithm is tested on random instances of the 15-puzzle and on path-finding problems. A significant improvement in efficiency is observed when compared with other bidirectional algorithms.