One way to distinguish among different varieties of supervaluationism is by their treatment of the entailment relation. Different versions of supervaluationism differ in their plausibility depending on whether particular intuitively plausible entailments and types of entailments are treated as valid, and on what notion of validity is employed. One important collection of entailments is exemplified by what a classical-style definition asserts. At least some classical-style definitions in terms of metaphysically necessary and jointly sufficient conditions are true, and thus we have in hand another criterion by which to judge competing supervaluationist accounts. The paper considers which accounts stand or fall given this criterion, and a general conclusion is that the criterion points away from all local notions of validity. The paper also considers the clash between intuitions in support of definitions and those for and against various supervaluationist accounts of validity, whether local or not.