Recent proposals hold that the cognitive systems underlying language production exhibit computational properties that facilitate communicative efficiency, i.e., an efficient trade-off between production ease and robust information transmission. We contribute to the cross-linguistic evaluation of the communicative efficiency hypothesis by investigating speakers’ preferences in the production of a typologically rare head-marking alternation that occurs in relative clause constructions in Yucatec Maya. In a sentence recall study, we find that speakers of Yucatec Maya prefer to use reduced forms of relative clause verbs when the relative clause is more contextually expected. This result is consistent with communicative efficiency and thus supports its typological generalizability. We compare two types of cue to the presence of a relative clause, pragmatic cues previously investigated in other languages and a highly predictive morphosyntactic cue specific to Yucatec. We find that Yucatec speakers’ preferences for a reduced verb form are primarily conditioned on the more informative cue. This demonstrates the role of both general principles of language production and their language-specific realizations.