Abstract Coalition structure generation has received considerable attention in recent research. Several algorithms have been proposed to solve this problem in Characteristic Function Games (CFGs), where every coalition is assumed to perform equally well in any coalition structure containing it. In contrast, very little attention has been given to the more general Partition Function Games (PFGs), where a coalition’s effectiveness may change from one coalition structure to another. In this paper, we deal with PFGs with positive and negative externalities. In this context, we identify the minimum search that is required in order to establish a bound on the quality of the best coalition structure found. We then develop an anytime algorithm that improves this bound with further search, and show that it outperforms the existing state-of-the-art algorithms by orders of magnitude