Nigerian Arabic has two structures for coding N + N relations: one in which the properties of the possessed noun are severely constrained and one in which the possessed and possessor nouns allow a full complement of modifiers. Similar to the methodology of Poplack and her collaborators (e.g., Sankoff, Poplack, & Vanniarajan, 1990), a normative distribution of nouns in the two possessive structures is established based on a corpus of monolingual (non-codeswitched) Nigerian Arabic texts. In a corpus of codeswitched texts, the distribution of English lexical insertions is found to deviate markedly from these normative patterns. The notion of iconicity is invoked to explain the skewed insertional patterns. It is hypothesized on the basis of various psycholinguistic studies that insertions from English are harder to access than are native lexemes. To compensate for slower access time, speakers match these insertions with the possessive structure that requires a minimal amount of manipulation for rapid embedding. This, it is shown, is the less iconic of the two possessive constructions. What emerges is a distinctive pattern of possessives characteristic of codeswitched Nigerian Arabic. After briefly testing the iconicity hypothesis against insertional patterns in Hausa and Standard Arabic, two other languages well attested in the codeswitched corpus, the question is addressed as to whether the codeswitched variety represents a code unto itself.