This paper follows on recent work (Iverson & Salmons 2004, 2007; Kiparsky 2005, 2006) seeking to resolve Kock's 1888 paradox intro-duced in his celebrated “period theory” of Old Norse i-umlaut. The basic finding is this: In paradigms where a phonological innovation has been rendered opaque by the operation of other sound changes, restructuring of the base form incorporates rather than derives the results of the innovation as it dies out; but if the innovation remains transparent in certain other paradigms, its expiration enables reversion to the antecedent phonological form. Both patterns can be subsumed under the traditional rubric of analogy, resulting in allomorphically uniform paradigms, but the former generalizes a sound change to con-texts in which it never occurred naturally, whereas the latter actually undoes, or reverses, a sound change.*