International Airlines Group (IAG) has built a reputation as one of the few large airline groups that knows how to make consolidation work. All its units—British Airways (BA), Iberia, Vueling, Level and Aer Lingus—are making healthy profits, at least partly due to IAG’s synergies and strict management control. The company, led by Willie Walsh, has also been successful since its creation in 2011 because it knew when to say no.