This article explores the role of the EU in unrecognised, also known as contested, states and more specifically, how their level of international recognition and empirical statehood (i.e. government authority and control) influence the EU’s engagement. By studying the case of the Turkish Republic of Northern Cyprus, the article finds that the EU engagement takes the form of ‘state avoidance’, mostly characterised by an effort to engage without endorsing state recognition and manifested via a) sui generis management of unrecognised borders, b) informal engagement with officials of the unrecognised state, c) replacement of public authorities with non-state actors and d) extensive engagement with civil society. In this regard, the article offers a range of causal explanations that can be tested across a greater number of similar cases. What is more, I contrast state avoidance to state-building approaches evident in aspiring states with more recognition but greater deficit of empirical statehood, such as Kosovo and Palestine, and I argue for a broader conceptualisation of the phenomenon of unrecognised states, allowing for variation in both the degree of recognition and of empirical statehood. As such, the article combines a discussion of rich empirical findings and inductive concept-building that contributes to a more informed discussion and further research development, especially as far as engagement from the EU is concerned.