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In this paper I argue that the notorious case of paradigm gaps, the first person singular gaps of Russian verbs, are not synchronically arbitrary as is often assumed (Graudina et al. 1976; Daland et al. 2007; Baerman 2008), but are predictable and connected to the opaque morphophonological alternations affecting stem-final consonants in the 1st person singular (1sg) present tense. I present evidence for a new empirical generalization showing that the problematic alternations in verbs are subject to a lexical conservatism effect (Steriade 1997). Namely, stems that appear in other derivationally or inflectionally related forms with the same alternation as the one expected in 1sg generally do not have gaps, while stems that have no attested related forms with alternations do. Overall, a larger set of verbs are problematic for the speakers than indicated in dictionaries, and there are degrees of “gappiness” with a lot of variation across speakers. Additionally, I consider how different theoretical proposals for handling ineffability fare in accounting for these findings. I propose to augment the framework of Harmonic Grammar (Legendre et al. 1990) with an additional post-competition step during which outputs can be compared to each other based on their Harmony scores. This proposal is not tied to violations of specific constraint and it has potential to account for both paradigm gaps and gradient grammaticality judgments.