Abstract Recent results show that both TAG and Minimalist grammars can be enriched with rational constraints without increasing their strong generative capacity, where a constraint is rational iff it can be computed by a bottom-up tree automaton. This raises the question which aspects of syntax can be adequately formalized using only such constraints. One of hardest phenomena commonly studied by syntacticians is binding theory. In this paper, we give a high-level implementation of (the syntactic parts of) binding theory in terms of rational constraints, and we argue that this implementation is sufficiently powerful for natural language. This conclusion is backed up by data drawn from English, German, and American Sign Language.