Miniature language learning is gaining increasing popularity to study biases underlying language universals. However, it is unclear whether learning preferences in these studies are influenced by learners’ native language. We ask whether a previously identified bias to balance production effort against message uncertainty holds across speakers of structurally different languages. We expose English (fixed order language without case) and German (flexible order language with case) speakers to miniature languages with optional case and either fixed or flexible constituent order and study their deviations from the input. We find that English and German speakers restructure the input in the same way: They match the input constituent order proportions and use more case in the flexible order language than in the fixed order language, thus following the bias to balance production effort against message uncertainty. Our findings suggest that this bias and its specific realization are independent of learners’ native language.