Is cognitive conflict detrimental to the development of innovative ideas in design teams, or is it a precondition for innovative performance? Assuming that there is a relationship between cognitive conflict and innovation, what kind of strategies do teams use in situations of cognitive conflict and what are the consequences for creativity? This paper reports on a study analysing how design teams cope with cognitive conflict during idea generation in an experiment. The design process was captured in protocols that were generated from video recordings. We report the results of the analysis of verbal protocols according to the five styles of (cognitive) conflict behaviour: competing, collaborating, compromising, avoiding and accommodating. Out of six teams, the results of the two highest and two lowest scoring teams are compared as regards innovation and functionality, which we see as the two components of creative outcomes. We show that design teams, even in a laboratory environment, encounter a considerable amount of cognitive conflict. A statistical comparison between the groups with the highest and the lowest innovative/functional design concept scores reveals significant differences in their conflict behaviour styles. The high innovation and high functionality groups used a more competing and a more compromising style, whereas groups rated low on the same parameters used a more collaborating style. The high rating groups on both creativity components used a more associating and rejecting behaviour style; the high innovation groups also generated more new ideas than the low innovation groups. The low rating groups on both innovation and functionality tended to repeat ideas more frequently. The main finding is that, in contrast with reports in previous research, the groups with higher innovation and functionality scores collaborated less than their peers in the low rating groups on these parameters. We interpret these results as signifying that creative performance in teams is not achieved mainly by agreement but needs cognitive confrontation.