If a classification (e.g., the distinction between bald and unbald things) is vague, then for some series of objects, (1) the classification does allow for a distinction between the extremal cases, and yet (2) it does not allow for a partitioning of the whole series, (3) nor do even any associated higher-order classifications (in terms of determinate truth) allow for such a partitioning. Or this is what a common conception of vagueness suggests (Russell (1923), Dummett (1975)). Standardly, this conception is cashed out more specifically in terms of borderline cases, which affect a classification as well as associated higher-order classifications (Wright (1987), Williamson (1994)). In his paper “The impossibility of vagueness” (2008), Kit Fine presents an argument, which suggests that this conception of vagueness is inconsistent. The previous literature offers various strategies of dealing with this result: by making problematic commitments regarding the logic for vague languages or the notion of determinate truth, or by reinterpreting vagueness in entirely new terms that do without the notion of a borderline case. In this paper, I present and defend a different strategy: According to this, vagueness is reducible to indeterminacy of any type of responses that encode a certain kind of conditional classificatory commitment. It is shown that on this account, we can block effectively Fine’s argument without needing to abandon the notion of a borderline case entirely, and without being hostage to problematic claims regarding the logic of vagueness or the notion of determinate truth. Time permitting, it will be also shown that the proposed strategy sheds new light on related earlier inconsistency results from higher-order gap principles (Wright (1987; 1992) and Fara (2002; 2003)).