End-to-end QoS has been seldom studied in its inter-domain aspects, particularly within the scope of the global Internet and from an engineering perspective. This paper is intended to be a contribution in this direction. Starting from a utopian model that achieves any kind of engineering operations without any specific constraint, we deduce the open issues andproblems to be solved by a viable inter-domain QoS model that could be deployed in operational networks. We provide some guidelines that will help the design of a QoS-based inter-domain Traffic Engineering solution. This paper is part of the work conducted within the IST MESCAL project.