Recent work on bidirectional search defined a lower bound on costs of paths between pairs of nodes, and introduced a new algorithm, NBS, which is based on this bound. Building on these results, we introduce DVCBS, a new algorithm that aims to to further reduce the number of expansions. Generalizing beyond specific algorithms, we then propose a method for enhancing heuristics by propagating such lower bounds (lb-propagation) between frontiers. This lb-propagation can be used in existing algorithms, often improving their performance, as well as making them "well behaved".