A substantially water free bleaching and/or highlighting composition for keratin fibres, especially human hair, comprising at least one compound with bleaching and/or highlighting effect and a polyhydroxy carboxylic acid as a chelating agent. Suitable and most preferred is gluconic acid and its salts especially mono valent cation salts such as sodium, potassium and ammonium salts. The composition can effectively bleach hair but cause less hair damage. Suitable compounds with bleaching and/or highlighting effect are sodium persulfate, potassium persulfate and ammonium persulfate. The composition may form part o a kit with aqueous composition comprising an oxidizing agent such as hydrogen peroxide and optionally a third composition comprising conditioning agent and/or direct dye.