The Hague Conference on Private International Law has engaged in a series of projects that, if successful, could provide the framework for critical aspects of trans-national litigation in the Twenty-first Century. Thus far, the work has resulted in the 2005 Hague Convention on Choice of Court Agreements and the 2019 Hague Convention on the Recognition and Enforcement of Judgments in Civil or Commercial Matters. Work now has begun to examine the need, desirability and feasibility of additional instruments in the area, with discussions of an instrument that would either require or prohibit the exercise of jurisdiction by national courts, and of an instrument that would channel parallel proceedings to a “better’ forum. The authors of this brief article advance the view that a convention regulating jurisdiction is not a good approach, but that an instrument finding a “better” forum in parallel proceedings, constructed on an open-minded and non-dogmatic basis, is needed, desirable, and feasible.