A number of recent accounts for vague terms postulate a kind of context-sensitivity, one that kicks in after the usual ‘external’ contextual factors like comparison class are established and held fixed. In a recent paper, ‘Vagueness without Context Change’(Mind 116 (2007): 275–92), Rosanna Keefe criticizes all such accounts. The arguments are variations on considerations that have been brought against context-sensitive accounts of knowledge, predicates of personal taste, epistemic modals, and the like. The issues are well known and there are variety of options available in reply. More important, the arguments rely on an overly narrow conception of context-sensitivity, suggesting that one size fits all. If Keefe’s arguments were cogent, they would tell against the context-sensitivity of just about any expression, beyond the typical indexicals, including the variation of vague terms with comparison class. However, the criticisms raised by Keefe do highlight certain questions that must be answered by an advocate of a context-sensitive account of vagueness, essentially the same sorts of questions that must be answered by a contextualist or relativist about knowledge, epistemic modals, predicates of personal taste, etc. The main purpose of this paper is to use replies to the relevant objections raised by Keefe as a springboard for further articulation of the underlying view of vagueness. © 2015 Taylor & Francis.