This paper analyses foot and syllable structure in Paumari, an Amazonian language of the Arawan family, all of whose languages are spoken near the Purus river in Western Amazonas state, Brazil. Paumari is a highly endangered language. The main descriptive and theoretical points I make in this paper are the following. First, Paumari has iambic feet, built from the right edge of the word. Second, these iambic feet are not weight-sensitive. These conclusions, if true, violate most proposals on prosodic feet. Perhaps the most interesting corollary of these points, though, is that the contrasts between trochaic and iambic foot structures are underdetermined by phonetics.  My next set of points are related to the Paumari syllable and syllable theory more generally. I argue that there is evidence that syllables in Paumari are irrelevant to stress placement. This leads us to a novel perspective on syllables, buttressed by additional data from the related Arawan language, Banawá. In particular I argue for a distinction between the syllable's role in the enhancement of segmental perception and the construction of the syllable as a domain for the application of phonological constraints.