We discuss problems inherent in domain specific tagging (biomedical domain) and their relevance to tagging issues in general. We present a novel approach to this problem which we call tagging with delayed disambiguation (TDD). This approach uses a modified, statistically-driven lexicon together with a small set of morphological, heuristic, and chunking rules which are implemented using finite state machinery. They make use of both delayed disambiguation and the concept of tag underspecification as an ordered sequence of tags.