The notion of ditransitivity is explored at the lexical, syntactic and surface levels. By focusing on several types of ditransitive sentences in Spanish it is revealed that there is a triple dissociation between these levels. First, it is shown that the availability of a ditransitive structure (syntactic level) for a certain verb does not depend on the verb being ditransitive (lexical level). Second, causative structures with dative arguments are shown to be ditransitive at the surface level, but not to have an underlying ditransitive structure. Finally, cases of unaccusative sentences with dative arguments are analysed as instances of ditransitive structures without lexical or surface ditransitivity. The paper argues that ditransitivity is at best a pre-theoretical, descriptive notion, and that ditransitive verbs in fact belong to Levin's (Papers from The Regional Meeting of the Chicago Linguistic Society 35: 223–247, 1999) non-core transitives: ditransitives are just transitives compatible with taking a relation between two individuals as complement. This analysis accounts for the intralinguistic and crosslinguistic variation in the expression of the relation, both in terms of type (two DPs related by a transitive preposition or an applicative head) and number of objects realized or omitted. Although the idea that there is no syntactic ditransitivity – that is, that no single verbal head can take two complements – has been implicit in most generative work of the last two decades, it has not been directly explored. This investigation leads to the conclusion that a syntactic property, binary branching, is at the basis of the impossibility of syntactic and lexical ditransitivity. Thus, this result suggests that syntax restricts not only possible structures but possible lexical meanings as well.