This paper examines a theory of vague language often taken to support supervaluationist logic, and argues that the theory supports subvaluationism equally well, which is to say not well at all. Instead, it's shown that the theory naturally gives rise to truth-functional theories of vague language. Two such theories are presented and evaluated; the theory based on the logic LP is preferred. A potential objection stemming from higher-order vagueness is examined and responded to. Finally, the import of an LP-based theory for the sorites argument itself is examined.