On the surface, bidirectional search (BDS) is an attractive idea with the potential for significant asymptotic reductions in search effort. However, the results in practice often fall far short of expectations. We introduce a new bidirectional search algorithm, Single-Frontier Bidirectional Search (SFBDS). Unlike traditional BDS which keeps two frontiers, SFBDS uses a single frontier. Each node in the tree can be seen as an independent task of finding the shortest path between the current start and current goal. At a particular node we can decide to search from start to goal or from goal to start, choosing the direction with the highest potential for minimizing the total work done. Theoretical results give insights as to when this approach will work and experimental data validates the algorithm for a broad range of domains.