This paper investigates a class of restrictive intermediate stages that emerge during L1 phonological acquisition, and argues that these stages are naturally accounted for within a gradual learning model that uses weighted constraints. The particular type of pattern of interest here – Intermediate Faithfulness (IF) stages – involves the preservation of marked structures just in privileged environments. We illustrate this with data from Bat-El (2007), which shows the innovation of morphologically-sensitive phonology during the acquisition of Hebrew. The resulting IF stage displays greater faithfulness in nouns – a privileged context (Smith 2000, 2001) – than in non-nouns. Like other IF stages, it emerges without any direct support from the target grammar (Revthiadou & Tzakosta, Rose 2000, Tessier 2007a).