This paper pursues the question what the implications of the Anti-Locality Hypothesis could be for the syntax of secondary predication. Focus of the discussion will be an investigation of what their internal structure of small clause complements must look like, how these small clause complements connect to their matrix environments, and what the relevance could be for the formulation of anti-locality presented here. Anti-locality is defined over a tripartite clause structure (split into three Prolific Domains) and a PF-condition on the computation (the Condition on Domain-Exclusivity). The investigation revolves around two leading questions: (i) does the syntax of small clauses involve more structure than simply [SC DP XP] and (ii) do small clauses constitute their own Prolific Domain (or maybe even more)? The results, affirmative answers to both questions, are also relevant for other types of secondary predication