Felicitous uses of contextually sensitive expressions generally have unique semantic values in context. For example, a felicitous use of the singular pronoun ‘she’ generally has a single female as its unique semantic value in context. In the present work, it is argued that contextually sensitive expressions have felicitous uses where they lack unique semantic values in context. The author calls such uses instances of felicitous underspecification. In these uses, the underspecified expression is associated with a range of candidate semantic values in context. A rule is provided for updating the Stalnakerian common ground when sentences containing felicitous underspecified expressions are uttered and accepted in a conversation. The author also gives an account of the mechanism that associates the range of candidate semantic values in context with an underspecified expression. Sentences containing felicitous underspecified expressions can be embedded in various constructions. The author considers the result of embedding such sentences under negation and verbs of propositional attitude. He also examines the question of why some uses of underspecified expressions are felicitous and others aren’t. This investigation yields the notion of a context being appropriate for a sentence (LF), where a context is appropriate for a sentence containing an underspecified expression if the sentence is felicitous in that context. Finally, some difficulties are covered that arise in virtue of the fact that pronouns and demonstratives have some sorts of implications of uniqueness that clash with their being underspecified.