Viruses that infect bacteria, called phages, are well-known for their extreme mosaicism, in which an individual genome shares many different parts with many others. The mechanisms for creating these mosaics are largely unknown but are believed to be recombinations, either illegitimate, or partly homologous. In order to reconstruct the history of these recombinations, we need to identify the positions where recombinations may have occurred, and develop algorithms to generate and explore the possible reconstructions.