In many situations it is difficult to avoid a conflict and cooperate with others, even when all parties would like to do so. We show that while having one coordination device tends to be beneficial, having more of them may actually make things worse. Our game theoretic analysis examines the relationship between two widely used coordination devices, namely the focal point and leadership. However, instead of conventional Stackelberg leadership we use a more general Stochastic leadership framework that allows for probabilistic revisions of the players' decisions. Upon observing the initial simulta-