An inflatable balloon for use in medical procedures includes a base balloon having a cylindrical section and a conical section and at least one circumferential fiber extending circumferentially around the conical section (see Fig 49C). The at least one circumferential fiber provides shape control of the base balloon upon inflation. The inflatable balloon includes a plurality of reinforcing strips in the conical section over the at least one circumferential fiber. Each reinforcing strip includes a plurality of fibers extending at an angle inclined relative to the at least one fiber. Each reinforcing strip is positioned a set circumferential distance away from a neighboring reinforcing strip. The reinforcing strips prevent the at least one circumferential fiber from falling or slumping down the tapered surface of the conical section.
