A medical balloon and a catheter utilizing the balloon (8) and a mechanism to attach the balloon (8) to the catheter tube, and method of making the balloon. The attachment mechanism forms a joint (10,11) and comprises a plurality of co-extruded and coextensive layers of different polymetric materials (8A, 8B, 20A, 20B) at least one of which is a base structural layer (8B, 20B) and the other of which (8A, 20A) is formed of polyethylene and copolymers thereof or of Selar. The base structural layer is thicker than the other layer. The attachment mechanism can be the balloon itself or it can be a sleeve (20A, 20B), either of which is heat sealed to the catheter tube (3). In either case, the diameter of the catheter at the joint (10,11) is substantially the same as the tube.
