The present falls within the field of cosmetics and relates to a cosmetic product for oxidatively changing the colour of keratinous fibres, particularly human hair. An exemplary cosmetic product includes (i) at least one cosmetic composition (KM) comprising (a) at least one oxidising compound, and (b) two or more thickening agents, and (ii) at least one cosmetic dye composition (FZ). The oxidising compound is a solid oxidising agent and is selected from the group of a percarbonate salt, a perborate salt and percarbamide salt. Further, the two or more thickening agents comprise an at least partially ionic polysaccharide and a substantially non-ionic polysaccharide. Also described is a method for dyeing hair.