In classic generative phonology (The Sound Pattern of English, Lexical Phonology) underlying representations and associated rules account for generalizations of two types: alternation-based generalizations and distribution-based generalizations. This article addresses the issue of how distribution-based generalizations are handled in Standard Optimality Theory and in Derivational Optimality Theory. The former uses the principle of the Richness of the Base, the latter relies on underspecification. It is argued that the Richness of the Base and the associated principle of Lexicon Optimization are unable to provide an adequate analysis of three types of generalizations: Nasal Assimilation in English, Vowel Retraction in the process of assimilating borrowings into Polish, and a presonorant voicing process called Cracow Voicing.