Assembly of the functional tetrameric form of phage Mu transposase (A protein) requires specific interactions between the Mu A monomer and its cognate sequences at the ends of the Mu genome (attL and attR) as well as those internal to it (the enhancer element). We describe here deletion variants of Mu A that show enhancer-independence in the assembly of the strand cleavage complex. These deletions remove the amino-terminal region of Mu A required for its interactions with the enhancer elements. The basal enhancer-independent activity of the variant proteins can be stimulated by a partner variant harboring an intact enhancer-binding domain. By exploiting the identical att-binding, and nonidentical enhancer-binding specificities of Mu A and D108 A (transposase of the Mu related phage D108), we show that the stimulation of activity is enhancer-specific. Taken together, these results suggest that the domain of Mu A that includes the enhancer-interacting region may exert negative as well as positive modulatory effects on the strand cleavage reaction. We discuss the implications of these results in the framework of a recent model for the assembly of shared active sites within the Mu A tetramer.