The Variable Hierarchy hypothesis of Dresher (2009) has a number of far-reaching consequences and applications – beyond the domain for which it was originally developed – including overspecification, kinship terminology, vowel reduction and whistled languages. On the other hand, the Contrastivity-Only Hypothesis of Dresher (2009) is, in its present form, empirically too limited once one looks at a full system of phonological processes within a language, and some reference to noncontrastive features seems inevitable. However, I outline a possible set of diagnostics and distinctions that might allow one to localize and limit the reference to noncontrastive features.
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Andrew Nevins (2015) studied this question.