It is argued that the analysis of stress placement in Piraha offers important new evidence on the proper characterization of prosodic organization and the notational devices necessary to express this organization. It is shown that Piraha stress placement is intractable to either a grid account or a binary branching analysis, but that an insightful perspective on a variety of stress-related phenomena is available if it is assumed that the language has ternary, obligatory branching feet. Evidence is presented from the assignment of stress in morphologically simple words, lexical compounds, words with extrametrical suffixes, and transmorphemic stress shifts and clash resolutions. (Author/MSE)