A multi-layered pipe of arbitrary length and cross-section is produced by co-extrusion of a segmented thermoplastic copolyester elastomer (COPE) outer body over the exterior surface of an annular tubular core of CPVC/PVC having a wall thickness, measured in the radial direction, in the range from about 0.95 mm (38 mils) to about 1.375 mm (55 mils). The COPE is cohesively bonded to the annular core coextensively with essentially the entire length of the pipe. Though the COPE is easily degraded in contact with water, and CPVC and blends of CPVC with less than 25% by weight of PVC are typically rigid when extruded as pipe, a laminated pipe of COPE and CPVC/PVC with the specified wall thickness and overall dimensions which in the laminated pipe satisfy an applicable plumbing code (SDR-11 in the U.S.) has essentially the same performance characteristics as commercially available CPVC pipe which is a monolayer and not a laminate.