|Abstract:||In this paper, I provide an analysis of ternary stress in Optimality Theory; specifically, I look at the five languages known to have an iterative ternary rhythm. A dialect of Bangla spoken in the Tripura region of India -- Tripura Bangla -- is one of these languages. Tripura Bangla is an interesting case to study because the current theory does not provide the sufficient tools for dealing with the particulars of its stress pattern. Specifically, the three-syllable lapses in words of the length 3n+1 syllables cannot be accounted for with *EXTENDED-LAPSE alone; I propose a new family of extended lapse constraints, synthesizing the qualities of positionally licensed lapse constraints, such as LAPSE-AT-END and LAPSE-AT-PEAK, and the usual *EXTENDED-LAPSE constraint. Specifically, I claim that in addition to *Extended Lapse, there are constraints licensing extended lapses word-finally and at the word peak -- EXTENDED-LAPSE-AT-END and EXTENDED-LAPSE-AT-PEAK respectively. I show that EXTENDED-LAPSE-AT-END is absolutely essential to the successful analysis of Tripura Bangla; there exists no other way of producing the observed stress pattern. These positionally licensed extended lapse constraints are an important aspect of Lapse Length Differentiation Theory (LLDT), the theory posited in this paper to explain all systems of ternary stress. LLDT consists of the ranking schema Extended Lapse Constraint >> Foot Economy Constraint >> Lapse Constraint. I also show that LLDT accurately predicts and accounts for the other known systems of ternary stress: Cayuvava, Estonian, Chugach Yupik, and Winnebago.