A special class of bound morphemes, called “floating” morphemes, is examined in the Apurinã (Arawak/Maipure) language of Brazil. These “floating” morphemes share both properties of affixes and of independent words in a manner reminiscent of cliticization phenomena. After comparing the ways that “floating” morphemes are similar and different from typical affixes and from typical independent words, the author investigates these special morphemes in the context of cliticization, arriving at two main conclusions: (i) although “floating” morphemes share a number of properties with clitic elements, they also pose a problem to the current typology of clitics, and (ii) they do not show the sort of uniform behavior expected from a class of special clitics, pointing to the need for a better understanding of the ways in which phonological forms can interact with the principles of organization of both word and sentence structures.