Apparatus and methods are provided for creating tubular devices, e.g., as components for catheters, sheaths, and or other devices sized for introduction into a patient. In one embodiment, a method is provided for making a tubular device using a sheet of material including a coated first surface. The sheet is rolled around a mandrel until longitudinal edges of the sheet are disposed near or adjacent one another, e.g., without attaching the longitudinal edges together. A tubular braid is positioned over the sheet-wrapped mandrel, one or more tubular segments are positioned over the tubular braid, and heat shrink tubing is positioned over the tubular segments. The resulting assembly is heated to cause the tubular segments to at least partially reflow and/or otherwise laminate the tubular segments to the tubular braid and sheet. The heat shrink tubing and mandrel are then removed to create the tubular device.