The European Union (EU) has, with increasing frequency, outlined an intention to strengthen its "digital sovereignty" as a basis for safeguarding European values in the digital age. Yet, uncertainty remains as to how the term should be defined, undermining efforts to assess the success of the EU's digital sovereignty agenda. The task of this paper is to reduce this uncertainty by i) analysing how digital sovereignty has been discussed by EU institutional actors and placing this in a wider conceptual framework, ii) mapping specific policy areas and measures that EU institutional actors cite as important for strengthening digital sovereignty, iii) assessing the effectiveness of current policy measures at strengthening digital sovereignty, and iv) proposing policy solutions that go above and beyond current measures and address existing gaps. To do this, we introduce a conceptual understanding of digital sovereignty and then empirically ground this within the specific EU context via an analysis of a corpus of 180 EU webpages that have mentioned the term "digital sovereignty" within the past year. We find that existing policies, in particular those pertaining to data governance, help to achieve some of the EU's specific aims in regard to digital sovereignty, such as conditioning outward data flows, but they are more limited concerning other aims, like advancing the EU's competitiveness and regulating the private sector. This is problematic insofar as it constrains the EU's ability to safeguard and promote its values. The policy solutions we propose represent steps towards the further strengthening of the EU's digital sovereignty and firmer protection of EU values. This paper is part of Governing "European values" inside data flows, a special issue of Internet Policy Review