Abstract: A method of finishing a glass surface to a close tolerance and a substantially blemish-free state using a moving polishing lap and an aqueous treatment liquid containing inert abrasive particles, in which the treatment liquid also contains a bifluoride which reacts with the glass to form an insoluble silicofluoride or fluoride, an acid supplying hydrogen ions and a solubility suppressant which ensures that the silicofluoride or fluoride separates out on the glass surface, whereby the lap and inert particles remove the silicofluoride or fluoride from high portions of the glass surface and thereby allow further reaction and glass removal in those areas until the desired finished form of the glass surface has been achieved, whereupon the supply of treatment liquid is stopped and immediately replaced by a supply of an alkaline neutralizing solution, e.g.