A catheter balloon is manufactured and prepared for use by heating a portion of a thermoplastic tube and pressurizing the lumen of the tube to cause the heated tube portion to stretch. Preferably, a central section of the tube portion is heated to a degree greater than the end sections of the tube portions, so that the central section of the tube portion expands to a thinner wall thickness than the end sections of the tube portion. Thus, when this newly formed, integral balloon is expanded within a patient, the central section thereof tends to expand outwardly first, ahead of the end sections. When such a balloon carries a tubular stent within the patient, the early expansion of the central section against a longitudinally centered stent causes a central portion of the stent to expand outwardly first, keeping the stent firmly centered on the balloon as it is expanded by the balloon.
