It is controversial which idioms can occur with which syntactic structures. For example, can Mary kicked the bucket (figurative meaning: ‘Mary died’) be passivized to The bucket was kicked by Mary? We present a series of experiments in which we test which structures are compatible with which idioms in German (for which there are few experimental data so far) and English, using acceptability judgments. For some of the tested structures – including German left dislocation, scrambling, and prefield fronting – it is particularly contested to what extent they are restricted by semantic factors and, as a consequence, to what extent they are compatible with idioms. In our data, these structures consistently showed similar limitations: they were fully compatible with one subset of our test idioms (those categorized as semantically compositional) and degraded with another (those categorized as non-compositional). Our findings only partly align with previously proposed hierarchies of structures with respect to their compatibility with idioms.