A method for preparing a blow molded plastic container having a thickened bottom structure from a plastic preform. The plastic preform and resultant container have a neck portion defining an opening, a tubular body portion depending therefrom and an integral bottom structure depending from the tubular body portion. A stretch rod is seated inside the preform. The stretch rod stretches the portions of the preform adjacent the bottom thereof by means of a controlled stroke, in an amount less than the amount of stretching of the tubular body portion, to impart to the container bottom structure and adjacent body portions continuous variations of wall thickness the thick parts thereof on average being thicker than the average wall thickness of the container body.