The goal of this thesis is to develop a restrictive theory of syllabic structure that dispenses with constituents. It starts with a review of previous approaches, discussing how syllabic structure has been characterised by constituent labels and/or dependency relations. Although the inventory of constituents may vary from one theory to another, the status of the syllable as the maximal constituent is taken for granted in most approaches. This thesis presents two types of argument against the syllable as a constituent. First, the thesis gives a prosodic analysis of reduplication in Micronesian languages that reportedly copies an initial consonant, verifying the claim put forward in Prosodic Morphology that reduplicative templates are prosodically constrained. I show how neither the specification nor the satisfaction of the reduplicative template needs to make reference to the syllable. The second argument concerns stress in Aranda, which is reported to fall on syllables with onsets. I put forward an alternative analysis in which stress requires a foot to begin with an onset. This foot-based requirement plays a role in a wide range of languages, not just in stress assignment but also in segmental-distributional restrictions. The absence of substantive evidence for the syllable as a constituent provides strong support for models of syllabic structure, such as Government Phonology, which dispense with a syllable node. However, similar arguments can be mounted against the subsyllabic constituents postulated in Government Phonology. Drawing heavily on Dependency Phonology, the present thesis shows how two types of dependency relation alone suffice to account for all of the significant regularities attributed to these constituents. The ultimate conclusion is that all syllabic constituency is redundant. Finally, from a theoretical base comprising the two rather different frameworks of Optimality Theory and Government Phonology, the thesis makes the following proposals. First, the principles and parameters approach and the constraint ranking approach should be integrated to capture categorical and relative well-formedness. Second, syllable structure is present in lexical representation and, in line with Structure Preservation, remains unchanged in phonological output.