Unification grammars (UG) are a grammatical formalism that underlies several contemporary linguistic theories, including Lexical-functional Grammar and Head-driven Phrase-structure Grammar. UG is an especially attractive formalism because of its expressivity, which facilitates the expression of complex linguistic structures and relations. Formally, UG is Turing-complete, generating the entire class of recursively enumerable languages. This expressivity, however, comes at a price: the universal recognition problem is undecidable for arbitrary unification grammars. We define a constrained version of UG that guarantees efficient processing, while allowing the expression of complex linguistic structures. We do so by proving that the constrained formalism is equivalent to Range Concatenation Grammar, a formalism that generates exactly the class of languages recognizable in deterministic polynomial time. We thus obtain a grammatical formalism that is on one hand highly expressive, and on the other efficient to compute with.