The ability to communicate complex meanings is a specific human ability which plays a crucial role in social interactions. A habitual example of these interactions is conversation. However, we observe that spontaneous conversation often hits an impasse when none of the interlocutors immediately produces a follow-up utterance. The existence of impasses in conversations, and the way that interlocutors overcome them provide evidence for our argument that conversation is a sequence of creative problem solving. In this work we use techniques from Conversation Analysis (CA) on publicly available databases of naturally-occurring speech and we suggest a framework to understand how impasses are reached and overcome. As a result, we hope to reveal yet another instance of the bond between language and creativity.