Current turn-taking approaches for spoken dialogue systems rely on the speaker releasing the turn before the other can take it. This reliance results in restricted interactions that can lead to inefficient dialogues. In this paper we present a model we refer to as Importance-Driven Turn-Bidding that treats turn-taking as a negotiative process. Each conversant bids for the turn based on the importance of the intended utterance, and Reinforcement Learning is used to indirectly learn this parameter. We find that Importance-Driven Turn-Bidding performs better than two current turntaking approaches in an artificial collaborative slot-filling domain. The negotiative nature of this model creates efficient dialogues, and supports the improvement of mixed-initiative interaction.