In a sequential bargaining game framework with complete information and no discounting, this paper proposes a mechanism in the spirit of a final offers arbitration (FOA). At each step, two parties may stop negotiating in order to implement a lottery between the two cur-rent proposals or go on making new proposals. A crucial difference with the FOA is that the list of past proposals is recorded and used by the mechanism. Once a lottery has been implemented, the parties can reject the offer which has been drawn and go back to a lottery between pro-posals made in the past. At the dominant subgame perfect equilibrium the two parties make gradual concessions leading to a final agreement which coincides with the Raiffa solution. The main incentive to reach an agreement comes from risk-aversion. The necessity to make step by step concessions generates evolving disagreement points and gradualism.