A method substantially completely oxidizing materials in which an aqueous stream bearing oxidizable materials is reacted with an oxidant comprising diatomic oxygen and at a temperature greater than the critical temperature of water and at a pressure greater than about 25 bar to produce a reaction product stream, and removing non-combustible inorganic constituents from the reaction product stream, including those which are highly soluble in liquid water below 374.degree. C., wherein the reaction is initiated in the presence of a rate enhancer comprising at least one oxidizing agent other than diatomic oxygen selected from the group consisting of ozone, hydrogen peroxide, salts containing persulfate, salts containing permanganate, nitric acid, salts containing nitrate, oxyacids of chlorine and their corresponding salts, hypochlorous acid, salts containing hypochlorite, chlorous acid, salts containing chlorite, chloric acid, salts containing chlorate, perchloric acid, and salts containing perchlorate.