A multicomponent packaging unit (kit-of-parts) for reductive decoloration of colored keratin fibers includes, presented separately from one another,a container (A) containing a cosmetic agent (a) anda container (B) containing a cosmetic agent (b). The agent (a) in container (A) (a1) includes one or more sulfinic acid derivatives from a particular group,(a2) includes one or more fatty constituents from the group of C12-C30 fatty alcohols, C12-C30 fatty acid triglycerides, C12-C30 fatty acid monoglycerides, C12-C30 fatty acid diglycerides, C12-C30 fatty acid esters, hydrocarbons and/or silicone oils,(a3) has a water content of at most 10.0% by weight, based on the total weight of the agent (a),the agent (b) in container (B) (b1) has a water content of at least 30.0% by weight, based on the total weight of the agent (b).Also, a method is for reductive decoloration of colored keratin fibers using the multicomponent packaging unit.