Through analyses of Russian voicing assimilation and German dorsal fricative assimilation, this paper 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 Optimality Theory undermines the assumptions of structure preservation and the principle has been widely rejected within OT. This paper 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. By using a solution that relies on stratal OT, this analysis also makes predictions about the interaction between non-structure-preserving phonological processes and morphological structure. Whereas there are cases of strict allophony, like German dorsal fricative assimilation, which have been shown to apply prior to the addition of word-level affixes, 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.