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Routing traffic subject to hose model constraints has been of much recent research interest. Two-phase routing has been proposed as a mechanism for routing traffic in the hose model. It has desirable properties in being able to statically preconfigure the transport network and in being able to handle constraints imposed by specialized service overlays. In this paper, we investigate whether the desirable properties of two-phase routing come with any resource overhead compared to: 1) direct source-destination path routing; and 2) optimal scheme among the class of all schemes that are allowed to even make the routing dynamically dependent on the traffic matrix. In the pursuit of this endeavor, we achieve several milestones. First, we develop a polynomial-size linear programming (LP) formulation for maximum throughput routing of hose traffic along direct source-destination paths. Second, we develop a polynomial-size LP formulation for maximum throughput two-phase routing of hose traffic for a generalized version of the scheme proposed in our previous work. Third, we develop a polynomial-size LP formulation for minimum-cost two-phase routing of hose traffic for the generalized version of the scheme. We also give a second (simpler) LP formulation and fast combinatorial algorithm for this problem using an upper bound on the end-to-end traffic demand. Fourth, we prove that the throughput (and cost) of two-phase routing is within a factor of 2 of that of the optimal scheme. Using the polynomial-size LP formulations developed, we compare the throughput of two-phase routing to that of direct source-destination path routing and optimal scheme on actual Internet service provider topologies collected for the Rocketfuel project and three research network topologies. The throughput of two-phase routing matches that of direct source-destination path routing and is close to that of the optimal scheme on all evaluated topologies. We conclude that two-phase routing achieves its robustn- - ess to traffic variation without imposing any appreciable additional resource requirements over previous approaches.