A production method for can cylinders, in which a circular blank of an aluminum sheet is deep-drawn to form a can cylinder that is open at one end; at least the outer lateral surface of the can cylinder that is open at one end is pretreated and coated, by at least the outer lateral surface of the can cylinder that is open at one end being brought into contact (i) with an acidic aqueous composition containing a) at least one water-soluble inorganic compound of the elements Zr, Ti, Si, Hf and/or Ce, and b) at least one water-soluble organic resin, which comprises at least hydroxyl groups, where the sum of the acid number and/or hydroxyl number of the respective organic resins is at least 50 mg KOH/g, and subsequently, with or without an intermediate rinsing step, is brought into contact (ii) with an aqueous dispersion of a wax, and (iii) is provided, with or without a rinsing step immediately following step (ii), with a protective coating, the binder of which is selected from acrylate and/or polyester resins; and in order to taper the diameter of the can cylinder in the edge region that is open at one end, the pretreated and coated can cylinder is drawn in and/or is shaped into a flange in the edge region that is open at one end. a circular blank of an aluminum sheet is deep-drawn to form a can cylinder that is open at one end; at least the outer lateral surface of the can cylinder that is open at one end is pretreated and coated, by at least the outer lateral surface of the can cylinder that is open at one end being brought into contact (i) with an acidic aqueous composition containing a) at least one water-soluble inorganic compound of the elements Zr, Ti, Si, Hf and/or Ce, and b) at least one water-soluble organic resin, which comprises at least hydroxyl groups, where the sum of the acid number and/or hydroxyl number of the respective organic resins is at least 50 mg KOH/g, and subsequently, with or without an intermediate rinsing step, is brought into contact (ii) with an aqueous dispersion of a wax, and (iii) is provided, with or without a rinsing step immediately following step (ii), with a protective coating, the binder of which is selected from acrylate and/or polyester resins; and (i) with an acidic aqueous composition containing a) at least one water-soluble inorganic compound of the elements Zr, Ti, Si, Hf and/or Ce, and b) at least one water-soluble organic resin, which comprises at least hydroxyl groups, where the sum of the acid number and/or hydroxyl number of the respective organic resins is at least 50 mg KOH/g, and subsequently, with or without an intermediate rinsing step, is brought into contact a) at least one water-soluble inorganic compound of the elements Zr, Ti, Si, Hf and/or Ce, and b) at least one water-soluble organic resin, which comprises at least hydroxyl groups, where the sum of the acid number and/or hydroxyl number of the respective organic resins is at least 50 mg KOH/g, and subsequently, with or without an intermediate rinsing step, is brought into contact (ii) with an aqueous dispersion of a wax, and (iii) is provided, with or without a rinsing step immediately following step (ii), with a protective coating, the binder of which is selected from acrylate and/or polyester resins; and in order to taper the diameter of the can cylinder in the edge region that is open at one end, the pretreated and coated can cylinder is drawn in and/or is shaped into a flange in the edge region that is open at one end.