This paper is another one to point up the usefulness of the relative utility approach in conflict management. In this case, it relates to the problem of stalemate. In this approach, each party involved is asked to identify the objectives which it perceives as relevant to it in considering any joint action that might lead to cooperation or tempering of the conflict. From their statements on objectives, cues and insights may be obtained on how to get around their stances on issues – stances (often very heated) that have resulted in the existing stalemate. The objectives, of course, often lie behind the issues. Typically, the greater the disaggregation (the specificity) of each party’s objectives, particularly when hierarchically ordered, the more cues and useful insights that can result. Once the objectives of a given party are identified, each party is asked to make pairwise comparisons of its objectives in order to obtain the relative importance of them. When there are logical inconsistences in their pairwise comparisons, this can be brought to the party’s attention, and often the party will adjust its statements to eliminate these inconsistences. But even when the party prefers not to do so, their statements can still be very useful. This brings up the point that both art and science are involved in effective mediation and management of conflict. It is, after all, the perceptions of the parties that matter, and not the views and knowledge of the mediator or third party trying to manage a conflict. And if in this way a joint action that leads to cooperation is found acceptable, it does not matter that it is not consistent with scientific knowledge. (Often science is based on logic and rationality that frequently are not characteristic of conflict behavior; and too often science is based on unrealistic assumptions, of which a scientist is often unaware.)Cues and insights that are derived directly or indirectly (even very indirectly) from pairwise comparisons may lead to wild ideas – ideas that observers of the conflict may consider far from reality, nonsensical, impractical, unscientific and the like, and often as failing to address conflict issues directly. This may be so even when the wild idea can be combined effectively with scientific concepts and knowledge to increase the probability of finding useful joint actions. But even by itself, a seemingly wild idea can generate a series of steps, perhaps at first far withdrawn from the issues, which in time is able to break the stalemate and lead to effective cooperation and major reduction, if not elimination, of the conflict. In the Kashmir study we come up with an idea initially viewed as very wild. From discussion with knowledgeable persons and with further thought, this idea was modified and gradually strengthened. We now offer it as a possible approach to joint activity that does not directly attack the Kashmir stalemate but has a real potential to lead to a series of small steps that in toto can help significantly to break this stalemate of long standing.