This paper investigates the time and space complexity of word order computation in the psycholinguistically motivated grammar formalism of Performance Grammar (PG). In PG, the first stage of syntax assembly yields an unordered tree ('mobile') consisting of a hierarchy of lexical frames (lexically anchored elementary trees). Associated with each lexica l frame is a linearizer—a Finite-State Automaton that locally computes the left-to-right order of the branches of the frame. Linearization takes place after the promotion component may have raised certain constituents (e.g. Wh- or focused phrases) into the domain of lexical frames higher up in the syntactic mobile. We show that the worst-case time and space complexity of analyzing input strings of length n is O(n5) and O(n4), respectively. This result compares favorably with the time complexity of word-order computations in Tree Adjoining Grammar (TAG). A comparison with Head-Driven Phrase Structure Grammar (HPSG) reveals that PG yields a more declarative linearization method, provided that the FSA is rewritten as an equivalent regular expression.