In this paper, I analyze an intricate morphological pattern in Murrinhpatha which involves reordering of the dual marker ngintha and an alternation in the form of its adjacent morpheme. I will argue that the pattern strongly suggests an analysis in Stratal Optimality Theory: first, phonological correlates of morphological structure provide evidence for cyclic domains within the word. Second, the phenomenon can be derived using independently motivated morphological constraints, thus supporting the idea that morphology is an independent module of grammar with different optimization mechanisms, but the same stratal split as phonology. The cyclic architecture of the word provides a straightforward explanation for the placement of the dual marker and the resulting allomorphy of the classifier stem without resorting to ad hoc mechanisms such as position classes. Furthermore, the cyclic structure neatly accounts for multiple exponence of [dual] through the daucal (dual/paucal) classifier stem and ngintha. My analysis suggests that this overexponence results from the blocking of ngintha in the first cycle and the selection of the featurally more specific daucal stem. However, ngintha is not strictly bounded to the first cycle, and its realization is delayed until the second cycle.