We discuss the problem of composing Quality-of-Service across several administrative domains considering an evolved DiffServ notion of Per-Domain Behavior (PDB). We discuss two components of the problem: path discovery and the effect of composing PDBs. We assume the most general scenario: domains are free to adopt any PDB, as long there are common semantics and a set of well-known QoS parameters (e.g. one-way delay, peak/sustained bandwidth, etc.). Thus we adopt an abstract representation of PDBs. We obtain three main results. First, we show that a distributed path discovery scheme is feasible and more scalable than a centralized one. Second, we show the outcome of inter-domain QoS composition, for general metrics and for Internet-alike topologies. Finally, and as an important practical result, we show that the Internet may not need a centralized governance model, in terms of the definition of inter-domain PDBs.