Transposition moves or copies specifically defined segments of DNA from one location to another. The transposon – the mobile DNA – is delineated by sequences at each end that mark its boundary. In many transposons, these ends are specified by DNA sequences to which copies of the transposase protein bind. To accomplish transposition, multiple copies of the transposase and accessory proteins synapse both ends of the transposon DNA into a transpososome, a large nucleoprotein complex. The transposase can then cleave the host-transposon DNA boundary and facilitate the joining of those ends to a new target site. Many transposons whose behavior has been studied in detail belong to the DDE family of transposition systems. In addition to many transposons, this family also includes the integrase proteins used by retroviruses to insert their viral DNA to their host’s genome. Although not related by sequence, the available high resolution structures of transpososome and intasomes from the DDE family show that they have converged on key strategies to ensure the fidelity of their transposition activity. Mu is an Escherichia Coli bacteriophage that replicates its genome using transposition. Its transposase, MuA, is a DDE transposase for which a high resolution transpososome structure has been solved. We have built on this structure and decades of MuA biochemical observations to test broadly-applicable hypotheses about how transposition is regulated. We have made the first precise in vitro measurements to test how altered DNA flexibility or conformations can modulate destination site DNA capture and attack. Bent or very flexible DNA is highly preferred as a destination, and continued bending after transposition is necessary to keep the transposon joined to its destination. This has direct implications for how DDE transposases and retroviral integrases select their target sites. We have also begun to de-convolute the subunit rearrangements that occur during Mu transpososome assembly process. Overcoming its intransigence towards traditional structural techniques, we have shown by crosslinking and SAXS that the MuA protein is constitutively a monomer prior to engaging Mu end binding sites. By combining this observation with the characterization of a mutant that dramatically accelerates assembly, we have proposed a more detailed pathway for the conformational changes that create a catalytically competent transpososome core.