In Differentiated Service (DiffServ) networks, the routing algorithms used by the premium class traffic, due to the high priority afforded to that traffic, may have a significant impact not only on the premium class traffic itself, but on all other classes of traffic as well. The shortest hop-count routing scheme, used in current Internet, turns out to be no longer sufficient in DiffServ networks. This paper studies the problem of finding optimal routes for the premium-class traffic in a DiffServ domain, such that (1) no forwarding loop exists in the entire network in the context of hopby-hop routing; and (2) the residual bandwidth on bottleneck links is maximized. This problem is called the Optimal Premium-class Routing (OPR) problem. We prove in this paper that the OPR problem is NP-hard. To handle the OPR problem, first, we analyze the strength and weaknesses of two existing algorithms (Widest-Shortest-Path algorithm and Bandwidth-inversion Shortest-Path algorithm). Second, we prop...