A method for making a tubular body (8, 10, 110, 210), comprising: providing a plurality of reinforcement carrying elements (72, 74) in a predetermined configuration relative to a central axis of a braiding apparatus; directing a primary mandrel along the central axis of the braiding apparatus such that the primary mandrel is surrounded by the plurality of reinforcement carrying elements (72,74); providing a source of a secondary mandrel at a first location adjacent to the primary mandrel and offset from the central axis; with the secondary mandrel feeding from the source at the first location, wrapping reinforcement members (6, 43) from the reinforcement carrying elements helically around a first portion of 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; moving the source of secondary mandrel to a second location (A2, A3); with the secondary mandrel feeding from the source at the second location, wrapping reinforcement members from the reinforcement carrying elements helically around a second portion of the primary mandrel such that either a) all of the reinforcement members also surround the secondary mandrel; or b) the secondary mandrel remains outside the reinforcement members; applying an outer jacket (7, 44) 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. providing a plurality of reinforcement carrying elements (72, 74) in a predetermined configuration relative to a central axis of a braiding apparatus; directing a primary mandrel along the central axis of the braiding apparatus such that the primary mandrel is surrounded by the plurality of reinforcement carrying elements (72,74); providing a source of a secondary mandrel at a first location adjacent to the primary mandrel and offset from the central axis; with the secondary mandrel feeding from the source at the first location, wrapping reinforcement members (6, 43) from the reinforcement carrying elements helically around a first portion of 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; moving the source of secondary mandrel to a second location (A2, A3); with the secondary mandrel feeding from the source at the second location, wrapping reinforcement members from the reinforcement carrying elements helically around a second portion of the primary mandrel such that either a) all of the reinforcement members also surround the secondary mandrel; or b) the secondary mandrel remains outside the reinforcement members; applying an outer jacket (7, 44) 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.