We explore the benefits of giving syllabic and segmental structure properties that parallel those of syntactic structure, including recursion, X-bar structure and the ‘light v’ structure of multi-argument constructs. Pursuing a radical version of Anderson’s structural analogy assumption, we show that assigning subordination structures to phonology – not just at the level of the foot but also within the syllable and even in the representation of segments – opens up explanatory perspectives on many a persistent question.