In Copala Triqui (Otomanguean; Mexico), words typically surface in isolation with a high tone (3, 4, 5, 31, 32) and surface with a low tone (1, 2, 13) in a number of syntactic environments (Hollenbach, 1984). Rodriguez & Bickmore (Forthcoming) accounts for high-low variations with a single underlying representation in the lexicon, sometimes with a floating low tone, that surfaces as high or low based on the cophonology associated with a given environment. This paper demonstrates how the cophonology account can be combined with the Cophonology by Phase framework (Sande et. al, 2020) to capture complex patterns in the tonal phonology of possessive constructions, which vary according to the alienability of the posssessum. Importantly, this CBP analysis can potentially be expanded to other lowering environments to allow for a less arbitrary implementation of cophonologies across multiple morphemes in the language, and unify syntactic contexts where tone lowering occurs.