The East-South geostrategic dilemma is a notorious source of tension in Europe, undermining defence cooperation within both NATO and the EU. This paper offers a proposal, seeking to address this dilemma through a new Permanent Structured Cooperation (PESCO) project. The Euro-Bases project would involve permanent arrangements and a sustained scheme to regularly rotate forces to shared military infrastructures located in the eastern and the southern neighbourhoods of Europe. Its primary aims would include signalling political solidarity in both directions, solidifying a 360-degree approach to threats and helping alleviate fears of abandonment among European partners. In the long term, through joint training in the field, the Euro-Bases project could contribute to the formation of a shared European strategic culture. Besides, by politically linking NATO’s territorial defence to the EU’s crisis management, it could contribute to EU-NATO convergence. The project could be prepared in 2020 by the three Weimar Triangle states – Poland, Germany and France – and remain open to all other interested states participating in PESCO. It could be launched with the fourth round of PESCO projects.