Multi-component packaging unit (kit of parts) for the reductive decolorization of dyed fibers, which comprises separately formulated (I) a container (A) containing a cosmetic agent (a) and (II) a container (B) containing a cosmetic agent (b), wherein agent (a) in container (A) includes (a1) one or more reducing agents (a2) one or more fatty components, and has (a3) a water content of no more than 10.0% by weight, based on the total weight of agent (a), and agent (b) in container (B) has (b1) a water content of at least 30.0% by weight, based on the total weight of the agent (b). The invention further relates to a method for reductive decolorization of dyed keratin fibers using the multi-component packaging unit.
