Transposition of phage Mu takes place within higher order protein-DNA complexes called transpososomes. These complexes contain the two Mu genome ends synapsed by a tetramer of Mu transposase (MuA). Transpososome assembly is tightly controlled by multiple protein and DNA sequence cofactors. We find that assembly can occur through two distinct pathways. One previously described pathway depends on an enhancer-like sequence element, the internal activation sequence (IAS). The second pathway depends on a MuB protein-target DNA complex. For both pathways, all four MuA monomers in the tetramer need to interact with an assembly-assisting element, either the IAS or MuB. However, once assembled, not all MuA monomers within the transpososome need to interact with MuB to capture MuB-bound target DNA. The multiple layers of control likely are used in vivo to ensure efficient rounds of DNA replication when needed, while minimizing unwanted transposition products.