The Gin recombinase of phage Mu selectively mediates DNA inversion between two inversely oriented recombination sites (gix) and requires the assistance of three accessory factors: negative supercoiling, an enhancer sequence, and the protein Fis. Deletion and fusion reactions are proscribed. Recombination by Gin is selective because it occurs only through a particular synaptic complex tailored for inversion. A single amino acid change in Gin allows it to carry out deletion and fusion as well as inversion and to dispense with the requirement for the accessory factors. We investigated the recombination mechanism of a mutant Gin protein by analyzing the knotted products of processive recombination by electron microscopy and gel electrophoresis. We find that, in sharp contrast to wild-type Gin, mutant Gin recombines through a broad spectrum of synaptic complexes that differ topologically. We propose a model for the selectivity of wild-type Gin recombination that explains how the dependence on the accessory factors limits recombination to inversion. In addition, we show that processive recombination by wild-type Gin is not restricted by the number of base-pairs separating the gix sites from each other and from the enhancer. This result can be explained if strand exchange proceeds through alternative paths dictated by the energetics of DNA coiling.