Statistical randomization tests in evolutionary biology often require a set of random, computer-generated trees. For example, earlier studies have shown how large numbers of computer-generated trees can be used to conduct phylogenetic comparative analyses even when the phylogeny is uncertain or unknown. These methods were limited, however, in that (in the absence of molecular sequence or other data) they allowed users to assume that no phylogenetic information was available or that all possible trees were known. Intermediate situations where only a taxonomy or other limited phylogenetic information (e.g., polytomies) are available are technically more difficult. The current study describes a procedure for generating random samples of phylogenies while incorporating limited phylogenetic information (e.g., four taxa belong together in a subclade). The procedure can be used to conduct comparative analyses when the phylogeny is only partially resolved or can be used in other randomization tests in which large numbers of possible phylogenies are needed.