Itunyoso Triqui (Oto-Manguean: Mexico) possesses several unique morphological derivations, each of which is typified by a toggling of glottal features at the right edge of the root. Root-final coda /ɦ/ is deleted if it is present on uninflected stems, but inserted if it is absent. This process, traditionally known as a morphophonological exchange rule (c.f. Baerman 2007; de Lacy 2012; Wunderlich 2012), is regular and productive in the language. Moreover, it is the primary exponent of the first person singular, the topical third person, and nominal quantifier morphemes, while tonal alternations are secondary, morpheme-specific exponents. The current paper both provides the first comprehensive description of these patterns in Itunyoso Triqui and argues two theoretical points. First, Triqui glottal toggling involves a morphophonological exchange mapping (/α/ → [β]; /β/ → [α]) which, in coordination with syllable well-formedness conditions, produces a toggling pattern. Second, exchange mappings or rules like the Triqui toggle pose unique problems for parallelist approaches to Optimality Theory but not to serialist approaches which permit intermediate stages of representation, a finding that accords well with the necessity for multiple strata in Triqui word formation.