The problem of finding least-cost reconstructions of past host/parasite associations, given the phylogenetic histories of a set of host taxa and of their associated parasites, is known to be complex. I provide in this article a new method of implicitly listing all the potentially optimal solutions to the problem, by considering each hypothesised past association individually, in a structure I have termed a Jungle. These structures are demonstrated to enable fast acquisition of globally optimal solutions under general weighting schemes, including minimisation of total number of postulated events and maximization of postulated cospeciation events. A simple example is given, and the pocket gopher/chewing louse system investigated by Hafner and Nadler [Hafner and Nadler, Nature 332 (1988) 258] is re-examined.