This paper reviews recent progress in the development of a computer-based system for supporting improvised group decision making in risky, time-constrained situations. One goal of this research is to realize a system design which is consonant with cognitively-grounded research on improvisation and which contributes to performance on representative tasks. Some of the issues and challenges involved in supporting creative but time-constrained decision making are first outlined. Salient constructs from research on cognition in improvisation, particularly in jazz, are next reviewed in order to frame the discussion of system design principles. The operationalization of these principles is next discussed. The paper concludes with a brief discussion of current work in the evaluation of the system and also outlines areas for further work.