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