The authors are very grateful to one associate editor, three anonymous referees, Will Cong, and Haoxiang Zhu whose comments helped to improve the paper significantly. The authors especially thank the European Financial Data Institute (EUROFIDAI) for providing access to the Base de données européennes à haute fréquence (BEDOFIH) data (data obtained via the EUROFIDAI Equipex PLADIFES ANR-21-ESRE-0036, within the framework of France 2030). The authors also thank Paul Besson, Dion Bongaerts, Julio Crego, Catherine d’Hondt, Thierry Foucault, Jose Miguel Gaspar, Carole Gresse, Alexander Guembel, Albert Menkveld, Giang Nguyen, Sebastien Pouget, Erik Theissen, and Marius Zoican as well as seminar participants at the Third Forum “Market Microstructure: Confronting Many Viewpoints”, at the conference of the Northern Finance Association (Charlevoix), at the Microstructure Exchange, at the Microstructure Online Seminars Asia Pacific, and at the IEX ARC conference as well as members of the Scientific Committee of the French Market Authorities (AMF) and, in particular, Philippe Guillot and Charles-Albert Lehalle, for providing useful comments. This paper previously circulated with the title “Does a preopen matter in fragmented markets?”.