This paper introduces a learning model to address the computational challenges arising from including highly abstract underlying representations (URs) in morphophonemic learning. The proposed learner structures the UR hypothesis space by disparity distance and considers potential URs in batches, beginning with fully concrete URs, only expanding the UR candidate space if the current set of UR candidates fails to meet a predetermined likelihood threshold. When expanding the UR candidate set, the learner uses markedness constraint weights and violation profiles to identify features that are potentially mis-specified underlyingly, limiting the generation of new URs to changes of those feature values. Overall, the learner inherently restricts abstraction to cases where introducing it demonstrably improves likelihood, while avoiding issues associated with the exhaustive search of an unbounded hypothesis space. Applied to Pakistani Punjabi a vowel nasality pattern, the model is shown to successfully acquire abstract URs for phonological patterns that parallel learners fail to capture.