In this paper we reexamine the prosodic system of Yidiji (Australian; Dixon 1977a, b; 1991) as a case supporting an approach to stress assignment in which the construction of bounded feet and the implementation of metrical heads within them occur as separate events (the SEPARABILITY hypothesis; Halle & Vergnaud 1987a,b (= H&V)). Specifically, we argue that a layer of feet assigned early in Yidiji phonological derivations is unheaded and insensitive to weight distinctions, and plays a role in allomorphy. Metrical heads are later assigned to these constituents by independent rules operating under quantity-sensitive principles. In other words, Yidiji employs an additive metrical system in which stressable heads are overlaid on existing foot structures (prosodic overlay). It is the interaction between the outputs of these operations which produces the flexible rhythmic structure for which Yidiji is known. This flexibility is exemplified by the forms in (la) and (lb) (from Dixon 1977a: 40–41), where stress falls on even-numbered and odd-numbered syllables respectively, counted from the left.