When I say “the theater is packed tonight” or “there are a lot of people in the theater tonight,” my utterance leaves a certain amount of uncertainty about the actual number of people in the theater. The same uncertainty is usually present when I say “the theater is full tonight” (even if the number of seats in the theater is known) or “there are 1000 people in the theater tonight.” In all cases, this can be traced back to the fact that we use and interpret utterances like these tolerantly: small differences in the actual number of people in the theater typically do not affect our willingness either to make these utterances or to accept a speaker's utterance of them. However, there is an important difference between the two sets of utterances: "the theater is full" and "there are 1000 people in the theater" can be used or understood in a way that is fully precise, but "the theater is packed" and "there are a lot of people in the theater" cannot be so used or understood. This distinction — the possibility of “natural precisifications” — is one of several empirical properties that distinguish vague terms like 'packed' and 'a lot' from (potentially) imprecise ones like 'full' and '1000'. The central theoretical question is how to account for these and other empirical differences while at the same time explaining why both kinds of expressions can be tolerant. Does the shared property of tolerance indicate that both vague and imprecise expressions have the same core semantic analysis (one in which all meanings are fundamentally tolerant); or does the difference in precisification reflect a core semantic distinction that is sometimes blurred by use? My goal in this talk is to present some arguments in favor of the latter position. I will begin by providing linguistic and experimental evidence which argues in favor of a distinction between vagueness as a fundamentally semantic phenomenon and imprecision as a fundamentally pragmatic one. I will then argue that any reasonable pragmatic model of imprecision is one that will give rise to the phenomenological properties associated with tolerance, for exactly the same reasons that the semantic features of vague terms give rise to these properties.