It has been observed that in languages with dominant-recessive harmony systems, while either roots or suffixes can be dominant (i.e., they can trigger a phonological change in their surrounding elements), prefixes are always recessive (Baković 2000, Casali 2003 a.o.). While the 'no dominant prefixes' hypothesis is acknowledged in most studies of dominant harmony systems, there is no systematic explanation for the pattern. Looking at the full affix inventory of three languages from three families (Kipsigis, Nilotic; Diola-Fogny, Niger Congo; Chukchi, Chukotko-Kamchatkan), an alternative is suggested in this paper, where the account is rooted in syntax: No Dominant High affixes. This relates to other proposals that posit syntactic constraints on phonological representations, even word-internally (Newell 2008, Fenger 2020). The proposal is that certain aspects of the phonological representation are fixed at a syntactically-determined point in the derivation (the first phase), and subsequent operations are restricted in the types of phonological change they may impose on the output of prior cycles. We contend that in the realm of vowel harmony, No Dominant High Affixes offers empirical advantages over No Dominant High Prefixes, including broader coverage extending to the patterning of suffixes and an account of certain attested dominant prefixes.