We augment the Nash bargaining solution by fairness ideals in order to predict the outcomes of unstructured bargaining after the individual production of a joint surplus. If production depends on individual effort, talent, and luck, fairness ideals might be based on the accountability principle. In a lab experiment with real production and unstructured bargaining, we investigate subjects’ fairness ideals, their bargaining behaviour, and the outcomes of the bargaining process. As impartial spectators, about 75% of the subjects hold meritocratic or libertarian fairness ideals. However, these ideals do not affect their bargaining behaviour which is strongly opportunistic. Therefore the fairness-augmented Nash solution with opportunistic fairness ideals predicts the bargaining outcome best.