This paper, developed within the frame of dynamic semantics combined with the precisification principle, proposes a new distinction between polysemy and vagueness. According to this distinction, a polysemous word is underspecified in relation to a set of lexicalized precisifications, whereas a vague word is underspecified in relation to a set of precisifications which are not lexicalized. It is also proposed that, notwithstanding the independence of denotative and argumentative levels, neither of these levels can be bypassed in the semantic representation. Key words: Dynamic semantics, Precisification, Underspecified, Denotative level.