Hierarchical A (HA) uses of a hierarchy of coarse grammars to speed up parsing without sacrificing optimality. HA prioritizes search in refined grammars using Viterbi outside costs computed in coarser grammars. We present Bridge Hierarchical A (BHA), a modified Hierarchial A algorithm which computes a novel outside cost called a bridge outside cost. These bridge costs mix finer outside scores with coarser inside scores, and thus constitute tighter heuristics than entirely coarse scores. We show that BHA substantially outperforms HA when the hierarchy contains only very coarse grammars, while achieving comparable performance on more refined hierarchies.