A method for bleaching dyed keratin-containing fibers, in particular human hair, characterized in that - a bleaching agent containing hydrogen peroxide in a cosmetic carrier is applied to the keratin-containing fibers, left on the fibers for 1 to 30 minutes and then rinsed out again, which fibers have been dyed using a dye that contains, in a cosmetic carrier, a combination of at least one CH-acidic compound, which is selected from at least one compound of the formula (CH-1) and/or from at least one compound of the formula (CH-2), in which • R 6 represents a linear or cyclic (C 1 to C 6) alkyl group, a (C 2 to C 6) alkenyl group, an optionally substituted aryl group, an optionally substituted heteroaryl group, an aryl-(C 1 to C 6) alkyl group, a (C 1 to C 6) hydroxyalkyl group, a (C 2 to C 6) polyhydroxyalkyl group, a (C 1 to C 6)-alkoxy-(C 1 to C 6) alkyl group, a group R I R II N-(CH 2) m -, in which R I and R" represent, independently of one another, a hydrogen atom, a (C 1 to C 4) alkyl group, a (C 1 to C 4) hydroxyalkyl group or an aryl-(C 1 to C 6) alkyl group, in which R I and R II can form a 5-, 6- or 7-membered ring together with the nitrogen atom, and m represents the integer 2, 3, 4, 5 or 6, • μR 7 represents a (C 1 to C 6) alkyl group, in particular a methyl group, • X - represents a physiologically acceptable anion, • the cycle of the formula (CH-1) represents all ring structures which can also contain additional heteroatoms such as nitrogen, oxygen or sulfur and can also carry uncondensed ring structures, all said ring structures being able to carry additional substituents, • Het represents an optionally substituted heteroaromatic compound, • X 1 represents a direct bond or a carbonyl group, and at least one reactive carbonyl compound, and - the bleaching agent is free of organic peroxo compounds and inorganic persalts. - a bleaching agent containing hydrogen peroxide in a cosmetic carrier is applied to the keratin-containing fibers, left on the fibers for 1 to 30 minutes and then rinsed out again, which fibers have been dyed using a dye that contains, in a cosmetic carrier, a combination of at least one CH-acidic compound, which is selected from at least one compound of the formula (CH-1) and/or from at least one compound of the formula (CH-2), in which • R 6 represents a linear or cyclic (C 1 to C 6) alkyl group, a (C 2 to C 6) alkenyl group, an optionally substituted aryl group, an optionally substituted heteroaryl group, an aryl-(C 1 to C 6) alkyl group, a (C 1 to C 6) hydroxyalkyl group, a (C 2 to C 6) polyhydroxyalkyl group, a (C 1 to C 6)-alkoxy-(C 1 to C 6) alkyl group, a group R I R II N-(CH 2) m -, in which R I and R" represent, independently of one another, a hydrogen atom, a (C 1 to C 4) alkyl group, a (C 1 to C 4) hydroxyalkyl group or an aryl-(C 1 to C 6) alkyl group, in which R I and R II can form a 5-, 6- or 7-membered ring together with the nitrogen atom, and m represents the integer 2, 3, 4, 5 or 6, • μR 7 represents a (C 1 to C 6) alkyl group, in particular a methyl group, • X - represents a physiologically acceptable anion, • the cycle of the formula (CH-1) represents all ring structures which can also contain additional heteroatoms such as nitrogen, oxygen or sulfur and can also carry uncondensed ring structures, all said ring structures being able to carry additional substituents, • Het represents an optionally substituted heteroaromatic compound, • X 1 represents a direct bond or a carbonyl group, and at least one reactive carbonyl compound, and • R 6 represents a linear or cyclic (C 1 to C 6) alkyl group, a (C 2 to C 6) alkenyl group, an optionally substituted aryl group, an optionally substituted heteroaryl group, an aryl-(C 1 to C 6) alkyl group, a (C 1 to C 6) hydroxyalkyl group, a (C 2 to C 6) polyhydroxyalkyl group, a (C 1 to C 6)-alkoxy-(C 1 to C 6) alkyl group, a group R I R II N-(CH 2) m -, in which R I and R" represent, independently of one another, a hydrogen atom, a (C 1 to C 4) alkyl group, a (C 1 to C 4) hydroxyalkyl group or an aryl-(C 1 to C 6) alkyl group, in which R I and R II can form a 5-, 6- or 7-membered ring together with the nitrogen atom, and m represents the integer 2, 3, 4, 5 or 6, • μR 7 represents a (C 1 to C 6) alkyl group, in particular a methyl group, • X - represents a physiologically acceptable anion, • the cycle of the formula (CH-1) represents all ring structures which can also contain additional heteroatoms such as nitrogen, oxygen or sulfur and can also carry uncondensed ring structures, all said ring structures being able to carry additional substituents, • Het represents an optionally substituted heteroaromatic compound, • X 1 represents a direct bond or a carbonyl group, and - the bleaching agent is free of organic peroxo compounds and inorganic persalts.