In collaborative planning activities, since the agents are autonomous and heterogeneous, it is inevitable that conflicts arise in their beliefs during the planning process. In cases where such conflicts are relevant to the task at hand, the agents should engage in collaborative negotiation as an attempt to square away the discrepancies in their beliefs. This paper presents a computational strategy for detecting conflicts regarding proposed beliefs and for engaging in collaborative negotiation to resolve the conflicts that warrant resolution. Our model is capable of selecting the most effective aspect to address in its pursuit of conflict resolution in cases where multiple conflicts arise, and of selecting appropriate evidence to justify the need for such modification. Furthermore, by capturing the negotiation process in a recursive Propose-Evaluate-Modify cycle of actions, our model can successfully handle embedded negotiation subdialogues.