This dissertation investigates the integration of two sources of non-conformity--exceptionality and variation - in a single phonological system. Exceptionality manifests itself as systematic non-conformity, and variation as partial or variable non-conformity. When both occur within the same phenomenon, this is particularly challenging for the linguistic system. Modern Hebrew spirantization provides an apt case study for the investigation of the interaction of these two sources of non-conformity where exceptional (non-alternating) segments are frequent, and variation in alternating segments has been reported (Adam 2002). This dissertation makes contributions in the forms of both data and analysis. Its goals are to provide a description of exceptionality and variation in Modern Hebrew spirantization and an analysis which incorporates alternation, exceptionality and variation. To collect data for the description of Modern Hebrew spirantization in verbal paradigms, an experimental rating task was conducted. Its goal was to examine speakers' acceptance of variation in both alternating and exceptional segments in Modern Hebrew spirantization, where stops and fricatives alternate, with the latter occurring in post-vocalic contexts and the former occurring elsewhere. The results establish that variation is at least somewhat acceptable in both alternating and exceptional segments, and is significantly more acceptable in alternating segments than in exceptional ones. Moreover, speakers showed a preference for the expected forms of both types of segments (i.e. the non-alternating form in exceptions, and post-vocalic fricatives or word-initial and post-consonantal stops in alternating segments). Importantly, the results also show that variation in both types of segments is gradient. To account for alternation, exceptionality, and variation in relation to a single phonological process, I propose a model combining the set-indexation approach for exceptionality (Pater 2000) with stochastic OT and the Gradual Learning Algorithm for gradience in variation (Boersma 1998, Hayes & MacEachern 1998, Zuraw 2000, Boersma & Hayes 2001, Hayes & Londe 2006). I call this the "combined model". I show that neither approach is able to account for both sources of non-conformity on its own; set-indexation allows only for categorical distinctions between alternation and exceptionality, whereas ranking distributions in stochastic OT limit the possible range of constraint interactions to account only for variation. Looking forward, implementing the acquisition of these patterns in current models of the learning algorithms results in a paradox. In particular, set-indexation and stochastic constraint rankings both presuppose that the mechanism they do not account for is established by a different mechanism - set-indexation is only implemented once variation and speech errors have been ruled out as the cause for non-alternation, whereas in order to provide the stochastic constraint rankings accounting for acceptability of variation in all tokens, set-indexation must have already been implemented. This study therefore opens new avenues for research involving learning algorithms and their handling of non-conformity. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]