Ab initio molecular orbital theory is used to investigate the coenzyme B-12-dependent reactions catalyzed by diol dehydratase. The key step in such reactions is believed to be a 1,2-hydroxyl migration, which occurs within free-radical intermediates. The barrier for this migration, if unassisted, is calculated to be too high to be consistent with the observed reaction rate. However, we find that "pushing" the migrating hydroxyl, through interaction with a suitable acid, is able to provide significant catalysis. This is denoted retro-push catalysis, the retro prefix signifying that the motion of the migrating group is in the direction opposite to the electron motion. Similarly, the "pulling" of the migrating group, through interaction of the spectator hydroxyl with an appropriate base, is found to substantially reduce the rearrangement barrier, importantly, the combination of these two effects results in a barrier reduction that is notably greater than additive. This synergistic interplay of the push and the pull provides an attractive means of catalysis. Our proposed retro-push-pull mechanism leads to results that are consistent with isotope-labeling experiments, with experimental rate data, and with the crystal structure of the enzyme.