A method for making a tubular body, comprising: directing a primary mandrel along a central axis of a braiding apparatus such that the primary mandrel is surrounded by a plurality of reinforcement carrying elements; directing a secondary mandrel adjacent to the primary mandrel and offset from the central axis; wrapping one or more reinforcement members (43, 243, 243', 443) from the reinforcement carrying elements helically around the primary mandrel such that some windings of the one or more reinforcement members surround the primary mandrel and pass between the primary mandrel and the secondary mandrel and some windings of the one or more reinforcement members surround both the primary and secondary mandrels; applying an outer jacket (7, 14) around the primary and secondary mandrels after wrapping the one or more reinforcement members therearound; and removing the primary mandrel to define a primary lumen within the tubular body, wherein wrapping one or more reinforcement members around the primary mandrel comprises braiding a plurality of reinforcement members around the primary mandrel, and characterized in that braiding the plurality of reinforcement members around the primary mandrel comprises: winding a first set of reinforcement members around the primary mandrel in a first helical direction such that some windings of the first set surround the primary mandrel without surrounding the secondary mandrel and some windings of the first set surround both the primary mandrel and the secondary mandrel; and winding a second set of reinforcement members around the primary mandrel in a second helical direction different than the first helical direction such that some windings of the second set surround the primary mandrel without surrounding the secondary mandrel and some windings of the second set surround both the primary mandrel and the secondary mandrel. directing a primary mandrel along a central axis of a braiding apparatus such that the primary mandrel is surrounded by a plurality of reinforcement carrying elements; directing a secondary mandrel adjacent to the primary mandrel and offset from the central axis; wrapping one or more reinforcement members (43, 243, 243', 443) from the reinforcement carrying elements helically around the primary mandrel such that some windings of the one or more reinforcement members surround the primary mandrel and pass between the primary mandrel and the secondary mandrel and some windings of the one or more reinforcement members surround both the primary and secondary mandrels; applying an outer jacket (7, 14) around the primary and secondary mandrels after wrapping the one or more reinforcement members therearound; and removing the primary mandrel to define a primary lumen within the tubular body, wherein wrapping one or more reinforcement members around the primary mandrel comprises braiding a plurality of reinforcement members around the primary mandrel, and characterized in that braiding the plurality of reinforcement members around the primary mandrel comprises: winding a first set of reinforcement members around the primary mandrel in a first helical direction such that some windings of the first set surround the primary mandrel without surrounding the secondary mandrel and some windings of the first set surround both the primary mandrel and the secondary mandrel; and winding a second set of reinforcement members around the primary mandrel in a second helical direction different than the first helical direction such that some windings of the second set surround the primary mandrel without surrounding the secondary mandrel and some windings of the second set surround both the primary mandrel and the secondary mandrel. winding a first set of reinforcement members around the primary mandrel in a first helical direction such that some windings of the first set surround the primary mandrel without surrounding the secondary mandrel and some windings of the first set surround both the primary mandrel and the secondary mandrel; and winding a second set of reinforcement members around the primary mandrel in a second helical direction different than the first helical direction such that some windings of the second set surround the primary mandrel without surrounding the secondary mandrel and some windings of the second set surround both the primary mandrel and the secondary mandrel.