We study the ability of several identical firms to collude in the presence of a more efficient firm, which does not take part in their collusive agreement. The cartel firms adopt stick-and-carrot strategies, while the efficient firm plays its one-period best-response function, regardless of the history of play. We characterize the most collusive symmetric punishment, which maximizes the scope for collusion. We then find that either a lower cost disadvantage or a smaller cartel size facilitates collusion. Finally, we compare our results with those obtained in the standard setup where all firms participate in the collusive agreement.