ABSTRACT – The preliminary reference brought to the Court’s attention in Anacco focuses on the possibility of not executing an EAW issued following a conviction after the criminal trial took place in the issuing Member State without the participation of a lawyer representing the requested person. Thus, the issue pertaining to the protection of fundamental rights is tackled for the umpteenth time. However, a further aspect comes to the fore, concerning the non-conformity of the executing Member State’s legal system with the provisions of a directive and the implications this might have for the execution of the EAW. Therefore, this topic is analyzed to ascertain whether the exceptional circumstances that make it possible to overcome the presumption deriving from the principle of mutual trust may also pertain to profiles that are not inherent to the protection of fundamental rights.