It is widely recognized that the will of the parties plays a determinant role in international commercial arbitration. An illustration of the uncontroversial central role enjoyed by party autonomy in arbitration, is given by the General Principle formulated by the International Law Association Committee on International Commercial Arbitration in its Final Report Ascertaining the Contents of the Applicable Law in International Commercial Arbitration: “First, the principal task of arbitrators in a commercial case is to decide the dispute within the mandate defined by the arbitration clause. Arbitration is a creature of contract. The parties can agree to its scope. That agreement is binding on the arbitrators”. This seems to leave no room for the arbitral tribunal to develop its own legal reasoning independently of the parties’ agreement. However, as I have observed elsewhere, numerous legal systems give the tribunal the power to make its own legal inferences from the submitted facts, and to independently interpret and apply the law. To a large extent, the tribunal also has the power to consider rules that do not belong to the law chosen by the parties—particularly when fundamental principles are at stake. These powers of independent legal reasoning only in few systems go so far as to permit the tribunal to order remedies different from those that were requested by the parties. Also, these powers have to be exercised cautiously and in the respect of the legal framework (particularly, of the principle of fair hearing). In many legal systems, thus, the tribunal is expected to inform the parties of its independent legal reasoning, so as to give them the possibility to make comments.