Tn3 resolvase is a site-specific DNA recombinase, which catalyzes strand exchange in a synaptic complex containing twelve resolvase subunits and two res sites. Hyperactive mutants of resolvase can form a simpler complex (X synapse) containing a resolvase tetramer and two shorter DNA segments at which strand exchange takes place (site I). We have solved the low-resolution solution structure of the purified, catalytically competent X synapse from small-angle neutron and X-ray scattering data, using methods in which the data are fitted with models constructed by rigid body transformations of a published crystallographic structure of a resolvase dimer bound to site I. Our analysis reveals that the two site I fragments are on the outside of a resolvase tetramer core and provides some information on the quaternary structure of the tetramer. We discuss implications of our structure for the architecture of the natural synaptic complex and the mechanism of strand exchange.