Liberal theories of justice typically claim that political institutions should be justifiable to those who live under them – whatever their values. The more such values diverge, the greater the challenge of justifiability. Diversity of this kind becomes especially pronounced when the institutions in question are supranational. Focusing on the case of the European Union, this article aims to address a basic question: what kinds of values should inform the justification of political institutions facing a plurality of value systems? One route to an answer is provided by John Rawls, who famously distinguishes between comprehensive and political values, and defends the exclusion of the former from the foundations of a political theory of justice. This article questions the tenability of the Rawlsian solution, and draws attention to an alternative twofold conceptual distinction: that between minimal and non-minimal and between substantive and procedural values. Minimal values are meant to be as independent as possible of controversial conceptions of the good and views of the world, regardless of whether these are comprehensive or purely political. It will be argued that their endorsement may thus further specify the nature of what should be shared in order to justify political institutions in conditions of pluralism. In order to refine further the account of such a basis of justification, two variants of minimalism will be presented according to whether they invest substantive or procedural values. Substantive values qualify the property of an outcome; procedural values qualify the property of a procedure. The latter part of the article consists of a ‘face-off’ between minimal proceduralism and minimal substantivism, considering reasons in favour of the adoption of each. The result, we suggest, is a helpful reorientation of the political dimension of the value debates to which the multiplicity of values amid contemporary European horizons give rise.