A composition for dyeing keratinous fibres comprises, in an aqueous carrier, (a) highly ethoxylated C16-C18 fatty alcohol(s) with from about 30 to about 100 ethoxy groups, (b) low-ethoxylated C16-C18 fatty alcohol(s) with 1 to 5 ethoxy groups, (c) optionally monoester(s) of glycerol and a C14-C20 fatty acid, (d) C16-C18 fatty alcohol(s), (e) alkalising agent(s), and (f) oxidation dye precursor(s), wherein—;the weight ratio of all highly ethoxylated C16-C18 fatty alcohols (a) to all low-ethoxylated C16-C18 fatty alcohols (b) is from about 10 to about 20, and the weight ratio of the sum of all constituents [(c)+(d)] to the sum of all ethoxylated fatty alcohols [(a)+(b)] is from about 2 to about 5. The present disclosure further relates to a multi-component packaging unit, in which the aforementioned composition is packaged separately from an oxidant preparation.