Through analyses of Russian voicing assimilation and German dorsal fricative assimilation, this article argues for a restricted version of structure preservation and a stratal model of Optimality Theory. Structure preservation ( Kiparsky 1985 ) prohibits the creation of allophones early in the phonological computation. The parallel architecture of OT undermines the assumptions of structure preservation, which has been widely rejected within OT. This article demonstrates that processes that are both neutralizing and non-structure-preserving, and which involve overlapping sets of targets and triggers, such as Russian voicing assimilation, result in a ranking paradox in parallel OT. Purely allophonic processes, such as German fricative assimilation, do not pose the same difficulties. Analyses of both processes are proposed within the framework of Stratal OT. The use of multiple strata eliminates the ranking paradox illustrated in Russian voicing assimilation and accounts for the interaction of German fricative assimilation and umlaut. This account predicts that non-structure-preserving neutralization cannot take place at the earliest level of evaluation but must apply after the rich base is filtered to the language-specific inventory and stem-level processes are applied. In the case of Russian, this is substantiated by application of assimilation across clitic boundaries, requiring phrase-level application.