We consider methods for handling incomplete (elliptical) utterances in spoken phraselators, and describe how they have been implemented inside BabelDr, a substantial spoken medical phraselator. The challenge is to extend the phrase matching process so that it is sensitive to preceding dialogue context. We contrast two methods, one using limited-vocabulary strict grammar-based speech and language processing and one using large-vocabulary speech recognition with fuzzy grammar-based processing, and present an initial evaluation on a spoken corpus of 821 context-sentence/elliptical-phrase pairs. The large-vocabulary/fuzzy method strongly outperforms the limited-vocabulary/strict method over the whole corpus, though it is slightly inferior for the subset that is within grammar coverage. We investigate possibilities for combining the two processing paths, using several machine learning frameworks, and demonstrate that hybrid methods strongly outperform the largevocabulary/fuzzy method.