It is a truism that people speak 'loosely' -- that is, they often say things that we can recognize not to be true, but which come close enough to the truth for practical purposes. Certain expressions, such as those including exactly, all and perfectly, appear to serve as signals of the intended degree of approximation to the truth. This article presents a novel formalism for representing the notion of approximation to the truth, and analyzes the meanings of these expressions in terms of this formalism. Pragmatic looseness of this kind should be distinguished from authentic truth-conditional vagueness.