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Abstract — In reconstructing the history of host-parasite associations, it is necessary to consider several different processes, such as cospeciation and host switching, that may affect an association. A simple reconstruction method is to maximise the number of host-parasite cospeciations. However, maximum cospeciation reconstruction may require the postulation of a large number of other kinds of events, such as parasite extinction or exclusion from certain hosts. A more sophisticated method associates each kind of event with a cost or weight which is inversely related to the likelihood of that kind of event occurring. I present a method of the latter type that distinguishes between two different processes: host tracking, of which cospeciation is a special case, and host switching. Given a relative weight for these two types of events, it is possible to convert the host phytogeny into a cost matrix, allowing for host switching, and use generalised-parsimony algorithms to find minimum-cost reconstructions of the history of the host-parasite association. Different relative switch weights give different minimum-cost reconstructions; the optimal switch weight can be found by maximising the fit between the tracking events and the parasite phytogeny, controlling for the number of postulated switches. As an empirical application of the method, data on an association between pocket gophers and their parasitic chewing lice were re-examined. Although these data have been extensively analysed previously, the generalised parsimony approach throws new light on the history of the association.