The phonology-phonetics interface is broadly concerned with the question of how abstract knowledge of a language's sound system influences and is influenced by the physical processes of producing and perceiving speech. There are a multitude of models that aim to address this question, many of which make distinct and even contradictory claims. This dissertation uses evidence from tone and phonation in San Martín Peras Mixtec (SMPM; ISO: jmx) to narrow the hypothesis space of viable frameworks of the interface, arguing that two basic characteristics must hold of any successful approach. First, drawing from phonetic and phonological analysis of a highly-specific process of low tone spread in SMPM, I argue that phonological and phonetic units of representation are defined at distinct levels of granularity, and therefore that they constitute distinct levels of representation. By extension, if any framework is to successfully derive low tone spread, it must incorporate different levels of representation for phonology and phonetics. Second, I show that a rate-driven, phonetic process of laryngeal reduction in SMPM influences the application of a phonological alternation, which provides evidence that the language's phonetic system is able to non-trivially influence which phonological output makes it to the surface. I argue that, in order to account for laryngeal reduction in SMPM, any successful model of the interface must allow for phonetics to influence phonology, though this influence must be indirect. Finally, I outline a model of Phonetically-Informed Candidate Selections (PICS) that embodies these characteristics and compare it with other frameworks that implement the required characteristics somewhat differently, outlining the distinct typological predictions and empirical coverage of each approach. Ultimately, this dissertation aims to constrict the hypothesis space of potential approaches to the phonology-phonetics interface, with the ultimate goal of pushing forward the field's understanding of the nature of language users' multi-tiered knowledge about the sound systems of their languages.