We present evidence that excision of the nonreplicative transposon Tn10 involves three distinct chemical steps, first-strand nicking, hairpin formation, and hairpin resolution. This three-step mechanism makes it possible for a single protein-active site to cleave two DNA strands of opposite polarity, as appears to be the case in this reaction. We infer the existence of alternating bifunctionality within the active site with suitable modulation of substrate components between steps. DNA double-strand breaks are also made by a "hairpin mechanism" in V(D)J recombination, possibly reflecting the same basic constraints faced in the Tn10 system. Similarities in the basic chemical steps in Tn10 transposition and V(D)J recombination suggest that the V(D)J mechanism may have evolved from a bacterial transposition system.