In the most commonly discussed cases, feature spreading is iterative, applying to all licit targets within a given domain. Early work within rule-based theories of phonology developed explicit mechanisms to induce both iterative and non-iterative patterns (e.g. Howard 1973; Anderson 1974). The issue of (non)iterativity has received as much attention in more recent work, with the notable exception of Kaplan (2008), which argues that both iterativity and non-iterativity are emergent concepts, and are always derivable from other forces at work in the grammar. In this paper we examine the status of non-iterativity, drawing on production data from Crimean Tatar. We argue that, in line with previous descriptions of the language, rounding harmony is truly non-iterative in the Central dialect of the language, and not derivable from other, independent constraints in the language. This finding is supported by evidence from several other languages, which all exhibit the same type of non-iterative spreading. We argue that the presence of these patterns demands a formal account, and we discuss the analysis of non-iterativity in both rule- and constraint-based theories, discussing their different predictions for the typology of feature spreading.