A multi-component packaging unit (kit of parts) for oxidatively coloring keratin fibers, including two preparations (A) and (B) packaged separate from each other. Preparation (A) includes, in a cosmetic carrier, (a1) at least one oxidation dye precursor and (a2) ammonia, and preparation (B) includes, in a cosmetic carrier, (b1) hydrogen peroxide, (b2) at least one fatty alcohol from the group comprising arachidyl alcohol (eicosan-1-ol), gadoleyl alcohol ((9Z)-eicos-9-en-1-ol), arachidonyl alcohol ((5Z,8Z,11Z,14Z)-eicosa-5,8,11,14-tetraen-1-ol), heneicosyl alcohol (heneicosan-1-ol), behenyl alcohol (docosan-1-ol), erucyl alcohol ((13Z)-docos-13-en-1-ol), and/or brassidyl alcohol ((13E)-docosen-1-ol), and (b3) at least one hydrocarbon having 8 to 80 C atoms.
