Random amplified polymorphic DNA (RAPD) data possess a number of undesirable features for parsimony analysis. These features include their non-codominant inheritance, their anonymous nature, their different (a)symmetrical transformation probabilities, and their possible GC priming bias. As a consequence, no single parsimony method seems appropriate for RAPD data. Moreover, the presence/absence coding of RAPDs is equivalent to the invalid independent allele model for allozymes. These issues are discussed and the way in which parsimony analysis of RAPDs can be misleading is illustrated. © 1995.