A hyperstable complex of the tetrameric MuA transposase with recombined DNA must be remodeled to allow subsequent DNA replication. ClpX, a AAAþ enzyme, fulfills this function by unfolding one transpososome subunit. Which MuA subunit is extracted, and how complex destabilization relates to establishment of the correct directionality (left to right) of Mu replication, is not known. Here, using altered-specificity MuA proteins/DNA sites, we demonstrate that transpososome destabilization requires preferential ClpX unfolding of either the catalytic-left or catalytic-right subunits, which make extensive intersubunit contacts in the tetramer. In contrast, ClpX recognizes the other two subunits in the tetramer much less efficiently, and their extraction does not substantially destabilize the complex. Thus, ClpX targets the most stable structural components of the complex. Left-end biased Mu replication is not, however, determined by ClpX's intrinsic subunit preference. The specific targeting of a stabilizing "keystone subunit" within a complex for unfolding is an attractive general mechanism for remodeling by AAAþ enzymes.