The invention concerns a method of producing a one-part piston which, in the region of the piston ring zone, has a closed cooling duct and a recess between the piston ring zone and the box-shaped piston body. The method comprises the following steps: A piston blank is produced by a forging process and the annular recess is produced by machining so that an upper part of the piston skirt remains connected to a radially inner region below the piston crown. The axial height of the recess corresponds at least to the axial height of the cooling duct. The cooling duct, which is open at the bottom, is produced by machining and hub bores are formed and the outer contour of the piston is finished. The cooling duct, which is open at the bottom, is closed by a two-part cover ring.