Dowling recently compared the empirical properties of Brooks parsimony analysis (BPA) and the leading method for studying phylogenetic aspects of coevolution, reconciled tree analysis (using the computer program TreeMap), based on a series of simulations. Like the majority of authors who have compared BPA with other methods, however, Dowling considered only the form of BPA proposed in 1981 and did not take into account various modifications of the method proposed from 1986 to 2002. This leaves some doubt as to the robustness of his assessments of both the superiority of BPA and its shortcomings. We provide a précis of the principles of contemporary BPA, including ways to implement it algorithmically, using either Wagner algorithm-based or Hennigian argumentation-based approaches, followed by an empirical example. Our study supports Dowling's fundamental conclusions about the superiority of primary BPA relative to TreeMap. However, his conclusions about the shortcomings of BPA due to inclusive ORing (i.e., the production of ghost taxa) are incorrect, as secondary BPA eliminates inclusive ORing from the method. Secondary BPA provides a more complete account of the evolutionary associations between the parasite groups and their hosts than does primary BPA, without sacrificing any indirectly generated information about host phylogeny. Secondary BPA of two groups of nematodes inhabiting Great Apes shows that TreeMap analysis underestimated the amount of cospeciation in the evolution of the nematode genus Enterobius.