The aim of this thesis is to explore the role of precisifications of vague predicates. Basically, the idea is that vague predicates can be, and are in fact, made more precise without altering their underlying concepts or truth-conditions. Vague terms and their precisifications are conceived as more or less precise instances of the same lexical entities. Precisifications are employed in several leading views on how we interpret and understand vague language, and how we utilize and reason with partial concepts and inexact knowledge—which covers most, if not all, human thinking and speaking. Although precisifications play important roles in the semantics of vagueness, they are not as straightforwardly understood as they might appear. There is more than one way to cash out the notion of precisifications, which have important implications for what extent various theories might be seen as a sufficient analysis of vagueness itself, as opposed to mere simulations of vagueness. Yet, many authors seem to have little concern for this issue. As a result, a term that is central to some of the most popular responses to vagueness might turn out to be ambiguous, if not vague. In chapter 1 I present and discuss the most vicious feature of vagueness: its tendency to generate paradoxes. This provides a general overview of the topic and introduces some important terms and concepts. Chapter 2 is a discussion of how to cash out the notion of precisifications, and not least admissible precisifications . I show that the notion is tied to the extensions of predicates. While extensions can be provided in terms of set theory, the notion of admissibility remains murky; beyond a certain point we are unable to separate the good from the bad precisifications. In chapter 3 I discuss Gottlob Frege s so-called sharpness requirement, and how it works to protect formal languages from vagueness. We see how Frege s conception of extensions as sets causes problems, and I question whether extensions are apt to characterize predicates at all. Finally we look at some of Frege s often overlooked views on ordinary language. In chapter 4 we consider a problem with the soritical arguments, which gives a fresh perspective on precisifications. I argue that precisifications provide no explanation of soriticality, and close off by briefly discussing the element of risk in theories of the semantics of vagueness.