This paper strengthens the claim first made in Smolensky & Goldrick 2016 that doubly conditioned phonological effects are best analysed as resulting from complex underlying morpheme representations that utilize Gradient Symbolic Representations. In addition, it is argued that such an item-based account of morpheme-specific phonology correctly predicts that doubly conditioned phonological effects are constrained by phonological locality: Cooperation between phonological elements is only possible if they are adjacent, i.e., if there is no unaffected element intervening between them. This latter claim is a direct response to Sande 2020 where the opposite claim is made that doubly conditioned phonological effects are constrained by phase-based locality and not phonological locality. The paper provides analyses for the three cases that are cited in Sande 2020 as a problem for an item-based account and shows that all three are perfectly compatible with a phonological locality restriction.