One of the most controversial issues in lexical semantics is the distinction between polysemy and indeterminacy/vagueness. We need to figure out whether a set of meanings are realizations of multiple senses of a word or manifestations of a single sense. There have been proposed many diagnostic tests for the distinction. Although they are useful to some degree, none of them are without problems. One of the reasons for these problems is that not all senses are equal on their statuses: there are not only full senses but also sub-senses. It seems to be impossible to set up a fixed set of all-purpose criteria for the distinction. For example, the level of sense discrimination for information retrieval would not have to be as deep as that for inference. In this study, we will focus on characterizing the hierarchical nature of (Korean) word senses, in due consideration of the conceptual units which are building blocks of senses.