In the past conversational recommender systems have adopted a similarity-based approach to recommendation, preferring cases that are similar to some user query or profile. Recent research, however, has indicated the importance of diversity as an additional selection constraint. In this paper we attempt to clarify the role of diversity in conversational recommender systems, highlighting the pitfalls of naively incorporating current diversity-enhancing techniques into existing recommender systems. Moreover, we describe and fully evaluate a powerful new diversityenhancing technique that has the ability to significantly improve the performance of conversational recommender systems across the board.