The Southern Bluefin Tuna (Jurisdiction and Admissihilily) Award of 4 August 2000 marked the first instance of the application of compulsory arbitration under Part XV, Section 2 of the 1982 UN Law of the Sea Convention and of the exercise by the Annex VII Tribunal of la compétence de la compétence pursuant to Article 288(4) over the merits of the instant dispute. The 72-paragraph Award is a decision of pronounced procedural complexity and significant multifaceted impacts of which appreciation requires an in-depth acquaintance with procedural issues of peaceful settlement of disputes in general and the-law-of-the-sea-related disputes in particular. Therefore, the article surveys first the establishment of and the course of proceedings before the five-member Annex VII Arbitral Tribunal, presided over by the immediate former ICJ President, Judge Stephen M. Schwebel, and also comprising Judges Keith, Yamada. Feliciano and Tresselt. Subsequently, the wide range of specific paramount questions and answers of the Tribunal are scrutinised against the background of arguments advanced by the applicants (Australia and New Zealand) and the respondent (Japan) during both written and oral pleadings, including in reliance on the extensive ICJ jurisprudence and treaty practice concerned. On this basis, the article turns to an appraisal of the impacts of the Arbitral Tribunal's paramount holdings and its resultant dismissal of jurisdiction with the scrupulous regard for the fundamental principle of consensuality. Amongst such direct impacts as between the parties to the instant case, the inducements provided by the Award to reach a successful settlement in the future are of particular importance. The Award's indirect impacts concern exposition of the paramount doctrine of parallelism between the umbrella UN Convention and many compatible (fisheries, environmental and other) treaties, as well as of multifaceted, both substantial and procedural effects of that parallelism. All those contributions will importantly guide other courts and tribunals seised in the future under the Convention's Part XV, Section 2.