Recently, the proposal of individual bounds that use consistent heuristics in front-to-end bidirectional search has improved the state of the art. However, modern theory in bidirectional search does not include algorithms that explicitly exploit consistency. Here we extend past theoretical work, namely must-expand pairs and derived concepts, to the case in which consistency is used, and clarify their relationship with the aforementioned individual bounds. Departing from the new theory, we show that consistent front-to-end heuristics can also be seen as an admissible estimation of the lowest cost of any path between any two nodes. Therefore, by grouping nodes by g and their heuristic values in buckets, such an estimate can be computed for sets of nodes and not individual pairs without loss of information. This bucket-to-bucket computation, although as expensive as front-to-front in the worst case, is the state of the art in the Pancake Problem, and allows implementing near-optimal algorithms that exploit consistency. Also, experiments offer an insightful measurement of how far front-to-end algorithms are from their theoretical limit.