The geometrical accuracy and surface roughness of diamond-turned workpieces is influenced by several parameters: the properties of the machine tool, the cutting process and the environmental conditions. A thin-walled electrode made from an aluminium alloy (wall thickness: 1 mm, length: 169 mm, outer diameter: 126 mm) and intended for an electrostatic measuring instrument, serves as an example to show how quasi-optical surfaces with a surface roughness Rα < 10 nm and deviations from roundness of ≤ 5 μm can be achieved when some of these influence quantities are optimized. The cylindrical part of the electrode was turned by means of a rounded mirror-finish diamond tool, the width of the cutting edge being 2 mm, the rake angle -6° and the clearance angle 2°. Compliance with the tolerances of geometrical accuracy was particularly difficult. As age-hardened wrought aluminium alloys cannot be stress-relieved by annealing, or only insufficiently, the geometrical accuracy - in particular the roundness - of thin-walled, rotationally symmetric bodies decisively depends on the state of stress of the workpiece material, on the clamping fixture and on the balanced condition of this clamping fixture.