Languages around the world share a number of commonalities known as language universals. We investigate whether the existence of some recurrent patterns can be explained by the learner’s preference to balance the amount of information provided by the cues to sentence meaning. In an artificial language learning paradigm, we expose learners to two languages with optional case-marking – one with fixed and one with flexible word order. We find that learners of the flexible word order language, where word order is uninformative of sentence meaning, use significantly more case-marking than the learners of the fixed word order language, where case is a redundant cue. The learning outcomes in our experiment parallel a variety of typological phenomena, providing support for the hypothesis that communicative biases can shape language structures.