The present invention relates to a method and a device for producing a preform with a base geometry optimized for the subsequent stretch blow molding. The preform produced in the injection mold is removed in a cooled removal sleeve and cooled in the shaft by intensive contact cooling, while to the greatest extent no cooling contact is made with the domed preform end due to a special contour of the cooling sleeve. On account of the re-heating of this domed end that is possible as a result, the latter can be mechanically deformed into a new geometry that is more advantageous for the blow-molding process, and consequently also influenced in the wall thickness. In the subsequent blow-molding process, such a deformed preform has primarily the advantage that the polymer material distributed better in the bottle can lead to considerable material savings and to bottle bases of a higher quality.