We explore targeted punishment as an explanation for collusion among many firms. We run a series of Cournot oligopoly experiments with and without the possibility of targeting punishment at specific market participants. In markets with two, four, six, and eight firms, we analyze to what extent targeted punishment helps firms to restrict output. We find that targeted punishment leads to more collusion across all markets. Furthermore, beyond two firms, this collusive effect turns out to be even stronger in markets with more competitors, suggesting a reversal of the conventional wisdom that collusion is easier with fewer firms.