The present invention is directed to a kit-of-parts for bleaching keratin fibers, comprising: an aqueous composition A comprising a) one or more non-acetylated sugar alcohol(s), and/or their mixtures, a bleaching composition B comprising b) one or more persalt(s) and/or peroxy salt(s), c) one or more alkalizing agent(s), and an aqueous oxidizing composition C, wherein the total concentration of compound(s) according to a) in the aqueous composition A is in the range of 1% to 50% by weight, calculated to the total weight of the aqueous composition A, and wherein the bleaching composition B comprises less than 5% by weight of water, calculated to the total weight of the bleaching composition B.