Polysynthesis in Inuit appears at both lexical and sentence levels. The analysis of a sampling of 3000 lexical entries and 300 affixes collected in Eastern Greenland (Tunumiisut) shows how polysynthesis works in lexical morphology and how phonetic wastage helps to obscure the motivation for some lexical forms and favors the development of homophones. Furthermore, the analysis of the full set of affixes reveals a number of formal and semantic similarities which relate affixes having different functions. This suggests a continuum over incorporating affixes, TAM verb affixes, and verb inflection, attested in a number of items. While the lexical origin of some incorporating affixes has already been suggested, the hypothesis of a larger lexical, derivational, and inflectional continuum may provide clues for discovering grammaticalization processes operating within the stock of affixes.