Coalition formation is an important form of interaction in multiagent systems. It enables the agents to satisfy tasks that they would otherwise be unable to perform, or would perform with a lower efficiency. The focus of our work is on real-world application domains where we have systems inhabited by rational, self-interested agents. We also assume an environment without any trusted central manager to resolve issues concerning multiple agents. For such environments, we have to determine both an optimal (utility-maximizing) coalition configuration and a stable payoff configuration, concurrently and in a distributed fashion. Solving each of these problems is known to be computationally expensive, and having to consider them together exacerbates the problem further. In this paper, we present our Progressive, Anytime, Convergent, and Time-efficient (PACT) algorithm for coalition formation to address the above concerns. We assess the stability of the resulting coalition by using a new stability concept, the relaxed core, which is a slight variation on the core. We show experimentally that our algorithm performs admirably in comparison to an optimal solution, it typically produces solutions that are relaxedcorestable, and it scales well.