The method for dewatering fleshings produced in leather production and treatment of fleeces comprises collecting them to form an aqueous alkaline suspension. The pH of the suspension is then lowered by successive addition of a weak acid, especially carbon dioxide. An independent claim is included for apparatus for carrying out the method comprising a process reactor (2) fitted with an injector for carbon dioxide, a control unit (3) for the amount of gas added and/or the pressure in the reactor and a mechanical dewatering unit (4) for removing water chemically separated from waste material in the reactor.