Reciprocals are characterized by a crossover of thematic roles within a single clause. Their peculiar semantics often creates special argument configurations not found in other clause types. While some languages either encode reciprocals by clearly divalent, transitive clauses, or clearly monovalent, intransitive clauses, others adopt a more ambivalent solution. We develop a typology of valency/transitivity mismatches in reciprocal constructions, based on a sample of Australian languages. These include: (i) monovalent clauses with a single ergative NP, (ii) mismatches between case marking and the apparent number of arguments, (iii) ergative marking on secondary predicates and instrumentals with an intransitive subject, and (iv) complex clause constructions sensitive to valency. Such mismatches, we argue, result from an "overlay problem": both divalent and monovalent predicates in the semantic representation of prototypical reciprocal scenes have had a hand in shaping the morphosyntax of reciprocal constructions.