Arbitrators are basically obliged to make decisions according to applicable substantive law. Most lex arbitri, however, allow for decision making according to principles of equity (ex aequo et bono) or for arbitrators to assess a dispute and act in proceedings as an amiable compositeur. An allowance to decide the merits ex aequo et bono doesnot mean to act as amiable compositeur and vice versa. Under French law, as the origin of amiable compositeur, this is a procedure where the arbitrators are to make decisions according to the law and legal principles, but they are entitled to alter the effects of the application of specific legal norms. Equity (equita) is only one of the dimensions of such decision making. This concept can be described as a process in search of the law and equity in order to find an equitable and possible solution. This approach has, however, undergone a significant transformation from the original concept in many jurisdictions. Unlike decision making as an amiable compositeur, which should mainly establish limits of applicability of the governing law and the method of application thereof for purposes of a fair hearing, ex aequo et bono is grasped in international practice as decision making praeter legem, in the domain of principles of morality and equity. In cases of equity, the focus is on the arbitrator’s subjective sense of justice.