Scholarly consensus sees EU supremacy as “necessarily bidimensional”: the supranational dimension necessarily stands alongside the national dimension, which rejects the absolute and unconditional supremacy of EU law. I argue that this view of bidimensional supremacy is conceptually flawed and descriptively inaccurate. On the conceptual side, I identify the fallacy of symmetry (the idea that national and supranational perspectives on supremacy are similar in nature and equally reductionist), the fallacy of selection (the view that bidimensionalism alone can overcome what it perceives as an inevitable subjective bias in the choice between national and supranational supremacy claims), and the fallacy of construction (an originally shared popular sovereignty theory, which turns out to be riddled with biases that disrupt the equilibrium within the internally divided sovereign). On the interpretative side, I suggest that the empirical evidence in support of bidimensional supremacy is weaker than it is generally assumed. I then offer an interpretation of the PSPP judgment of the German Federal Constitutional Court, which holds a judgment of the Court of Justice of the European Union to be ultra vires, unlawful and thus non-binding. PSPP presents a problem of German origins and cast, rather than one stemming from the inner structure of EU constitutionalism. At most, PSPP represents a contingent, rather than necessary, and thus unexceptional instance of bidimensional supremacy.