This paper analyzes how the European Court of Human Rights has reacted to the progressive developments by the European Union of its own human rights standards through the Charter of Fundamental Rights and an increasing number of secondary law instruments. These evolutions have been welcomed by ambivalent reactions from Council of Europe institutions. Voices in Strasbourg have denounced a risk that autonomous EU fundamental rights standards might create dividing lines in Europe and lead to a "multi-speed" Europe of human rights. Yet, addressing this concern through an alignment of the EurCourtHR case law on EU law developments might result in imposing majority value choices on the minority of Council of Europe members. The paper assesses the well-founded character of these apprehensions in light of two ongoing case law tendencies. First, the mechanisms established to reflect the specificities of EU law in assessing Member States’ liabilities under the ECHR are increasingly being challenged, both in the Strasbourg case law and as a consequence of the evolution of EU law itself. Second, the Strasbourg Court has relied on EU law in the application of the consensus and margin of appreciation doctrines, with some separate opinions advocating for a more influential role for EU law. The "interoperability" between the EU and the ECHR legal order may, however, be questioned in light of the different methodologies followed by the two European supranational courts and the limited "consensual" value of EU law in the sense of the EurCourtHR case law. In order to avoid curtailing the consensus and subsidiarity foundations of the Convention, it is submitted that the Strasbourg Court should pay due attention to the exact consensual value of each specific provision of EU law. In that respect, the Luxembourg Court could provide valuable support in maintaining, where relevant, a visible link between the human rights developments initiated at EU level and the specific objectives of the EU integration project.