We study the rheology of polymers and other entangled fluids at high shear rate, where reptation theories (such as that of Doi and Edwards) predict, unphysically, a decreasing shear stress. A modification of the tube model, based on the concept of a dumbbell confined to a pipe, was recently proposed by Cates, McLeish, and Marrucci (Europhys. Lett. 1993, 21, 451). We show that their heuristic calculations correspond to a situation where the transverse dimension DELTAy of the dumbbell (perpendicular to the tube) remains constant in time. We perform an exact analysis, allowing DELTAy to fluctuate subject to the constraint of the pipe, and also study a more detailed model-a Rouse chain confined to a pipe. We find that the two dumbbell models give different results from each other and from the Rouse chain. We discuss briefly the relation between this work and experiments on entangled polymeric and micellar systems.