The present application relates to means the persistence of at least one nonionic component having an hlb of less than or equal to 8,0, as well as the combination of a blue and of a red substantive dye, wherein the weight ratio of the blue dyes relative to the red dyes is greater than 1. Furthermore, means for the bleaching of human hair, additionally containing at least one oxidizing preparation and, if appropriate, a bleaching composition force amplifier. By the compositions according to the invention, it has become possible undesired color shifts during the bleaching and reddish hues in yellowish to avoid.
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