Technology sovereignty has become a central EU policy objective, as well as a core idea behind a particular regulatory strategy devised for EU technology policies, including the policy on artificial intelligence. However, technology sovereignty raises complex problems that burdens policy-makers with dilemmas rather than clear-cut solutions. The EU’s policy approach and its chosen regulatory strategy seem to ignore the complexities inherent in technology sovereignty and maintain that the EU, unaffected by the dilemmas, can adopt an appropriate response. The EU’s strategic choice of introducing a high-standard, value-driven regulation of technology markets, including the European market for AI systems, faces another, partly related problem. EU regulatory measures, which interfere directly and in divergent ways with national industrial and economic policy, need to be adopted using the competences and the decision-making framework available, which put their own restraints on the regulatory outputs. The AI Act is a measure of EU technology regulation that bears the mark of these origins. Although it pursues ambitious general objectives, including those derived from technology sovereignty, it reads as a conventional internal market product safety measure. It is a product of practical compromises rather than of grand strategic choices, which may disappoint the expectations originally linked to it.