Competitive hierarchies in diverse ecological communities have long been thought to lead to instability and prevent coexistence. However, system stability has never been tested, and the relation between hierarchy and instability has never been explained in complex competition networks parameterised with data from direct observation. Here we test model stability of 30 multispecies bryozoan assemblages, using estimates of energy loss from observed interference competition to parameterise both the inter- and intraspecific interactions in the competition networks. We find that all competition networks are unstable. However, instability is mitigated considerably by asymmetries in the energy loss rates brought about by hierarchies of strong and weak competitors. This asymmetric organisation results in asymmetries in the interaction strengths, which reduces instability by keeping the weight of short (positive) and longer (positive and negative) feedback loops low. Our results support the idea that interference competition leads to instability and exclusion but demonstrate that this is not because of, but despite, competitive hierarchy.