|Abstract:||Yukatek Maya has two phonological phenomena, allophonic aspiration and [h]-epenthesis, which insert the feature [spread glottis] at the right edge of the prosodic word and phonological phrase respectively. Providing an OT analysis, then, requires constraints which privilege [s.g.] in certain `weak' positions. This sort of constraint, however, conflicts with many theories of positional privilege since it prefers a marked form in a ‘weak' position. Despite this, we show that a limited class of such constraints are necessary to account for aspiration and [h]-epenthesis in Yukatek Maya. Furthermore, these processes are argued to instantiate a cross-linguistic pattern favoring certain laryngeal features at the right edge of larger prosodic constituents. This pressure, which we term Final Laryngeal Strengthening, is argued to be the phonologization of a gradient phonetic pressure: the articulatory effort required to maintain persistent voicing throughout longer prosodic units.