We studied the mechanism of recombination by determining the structure of the products of the phage lambda Int system. Electron microscopy of RecA-coated products revealed only knots and catenanes containing a regular right-handed spiral structure. The structure and distribution of products establish that the recombination sites pair by essentially random collision, rather than by tracking. However, the distribution also indicates that the binding of the enzyme must introduce nonrandom components into the reaction and stabilize at least two additional supercoils that become links in the product. Moreover, the regularity of the structures indicates that the strand exchange is accomplished in a very simple way, introducing only a single link into the product. All other links result from the direct conversion of substrate supercoils into knot and catenane links. These supercoils must be in a right-handed, braided form, rather than solenoidally wound as in nucleosomes.