This paper describes and analyses the pattern of word stress found in the standard dialect of Koshur (Kashmiri) spoken in Srinagar. The significance of Koshur for studies of stress lies in that taken together, its pattern of stress assignment and a pervasive pattern of syncope conspire to produce a four-way syllable weight distinction that has sometimes been expressed as the scale CVːC>CVː>CVC>CV. The interesting feature of this type of scale is that closed syllables, CVːC and CVC are preferred as stress peaks over open syllables with vowels of the same length. Other researchers have noted that in languages with this scale, or the abbreviated ternary version CVː>CVC>CV, CVC syllables behave ambiguously with respect to stress. They seem to be heavy in relation to CV when CVː syllables are absent. In a stress clash context however, CVC defers to CVː. ‘Mora-only’ accounts of other languages with this scale have interpreted the ambiguous behaviour of CVC as evidence that CVC syllables are bimoraic where their behaviour seems to group them with CVː but monomoraic elsewhere (e.g. Rosenthall & van der Hulst 1999, Morén 2000). To account for the CVːC>CVː effect, mora-only accounts have been forced to assume that CVːC are trimoraic. We show that a mora-only analysis does not offer a satisfying account of the Koshur facts, and we argue instead that the origin of the CVC>CV and CVːC>CVː effects is the presence of a coda that branches from the final mora of a syllable, making the closed syllables more harmonic as prosodic heads. Under this view, branchingness emerges as another dimension of the mora, along with moraic quantity and the quality of segments linked to moras, which contributes to syllable prominence.