In this article we examine patterns of root allomorphy in Greek that involve vowel alternations and propose a Generalized Non-linear Affixation (Bermúdez-Otero 2012) analysis according to which these alternations result from the competition between segments that belong, on the one hand, to the vocabulary items of roots and, on the other, to the exponents of functional heads (Voice/Aspect, n). More specifically, we claim that phonological entities have a gradient degree of presence in a structure, that is, are specified with a certain activation strength value underlyingly (Smolensky and Goldrick 2016). As a result, the surface realization of roots is determined by the relevant activation level of the exponents of functional heads they are eventually combined with. From all available exponents, the one that optimally complements the strength value of the vocabulary item of a given root will eventually surface. Our analysis is shown to be theoretically advantageous because it develops a strictly phonological account of allomorphy and, moreover, it captures the attested generalizations without resorting to extensive stem/span listing or to the application of phonologically unrestricted readjustment rules.