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In this article I propose a new construction algorithm for the phonological word in Hungarian. Based on a detailed discussion of the di¤erences between so-called ‘postpositions’ and ‘case su‰xes’, I show that both types of adpositional elements are of the same morphosyntactic category, and that phonological word status depends not on an arbitrary division between a‰xes and syntactically free items, but on phonological properties of the respective adpositions: Bisyllabic adpositions form phonological words on their own, while monosyllabic adpositions are integrated into the phonological word of their lexical head. Generalizing this result, I argue that all functional elements of Hungarian traditionally called ‘inflectional a‰xes’ are syntactically independent functional heads integrated into the phonological word of a preceding lexical head because they are prosodically too small. I show that apparently bisyllabic inflectional a‰xes must either be decomposed into di¤erent markers or are underlyingly monosyllabic, and develop a ranking of optimality-theoretic alignment constraints implementing the construction algorithm for the phonological word in formal detail.