In this article I propose a new construction algorithm for the phonological word in Hungarian. Based on a detailed discussion of the differences between so-called 'postpositions' and 'case suffixes', 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 affixes 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 affixes' 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 affixes must either be decomposed into different 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.