Evolving networks with a constant number of edges may be modelled using a rewiring process. These models are used to describe manyreal-world processes including the evolution of cultural artifactssuch as family names, the evolution of gene variations, and thepopularity of strategies in simple econophysics models such as the minority game. The model is closely related to Urn models used forglasses, quantum gravity and wealth distributions. The full meanfield equation for the degree distribution is found and its exactsolution and generating solution are given.