An agent for lightening keratin fibers, characterized in that it contains, in a cosmetic carrier: (i) at least one oxidizing agent selected from hydrogen peroxide and/or one of the solid addition products thereof with organic or inorganic compounds, and (ii) at least one sulfonimine of formula, in which R1 to R6 represent, independently of one another, a hydrogen atom, a halogen atom, a C 1 -C 6 alkyl group, a partly or completely halogenated C 1 -C 6 alkyl group, a C 2 -C 6 alkenyl group, a C 1 -C 6 hydroxyalkyl group, a C 2 -C 6 polyhydroxyalkyl group, a C 1 -C 6 alkoxy group, a C 1 -C 6 alkoxy C 2 -C 6 alkyl group, an aryl C 1 -C 6 alkyl group, a hydroxy group, a nitrile group, a nitro group, a carboxylic acid group, a sulfonic acid group, a sulfonamido group, an amino group, a di C 1 -C 6 alkylamino group, a mono C 1 -C 6 alkylamino group, a C 1 -C 6 alkoxycarbonyl group, an optionally substituted aryl group, or an optionally substituted heteroaryl group, two functional groups selected from the group R1, R2 and R3 and/or two functional groups selected from the group R4, R5 and R6 each being able to form, with one another and with the adjacent benzene ring, a fused aromatic or heteroaromatic five- or six-membered cycle, characterized in that at least N-[(4-methoxyphenyl)methylidene]benzenesulfonamide is contained as the sulfonimine according to formula. (i) at least one oxidizing agent selected from hydrogen peroxide and/or one of the solid addition products thereof with organic or inorganic compounds, and (ii) at least one sulfonimine of formula, in which R1 to R6 represent, independently of one another, a hydrogen atom, a halogen atom, a C 1 -C 6 alkyl group, a partly or completely halogenated C 1 -C 6 alkyl group, a C 2 -C 6 alkenyl group, a C 1 -C 6 hydroxyalkyl group, a C 2 -C 6 polyhydroxyalkyl group, a C 1 -C 6 alkoxy group, a C 1 -C 6 alkoxy C 2 -C 6 alkyl group, an aryl C 1 -C 6 alkyl group, a hydroxy group, a nitrile group, a nitro group, a carboxylic acid group, a sulfonic acid group, a sulfonamido group, an amino group, a di C 1 -C 6 alkylamino group, a mono C 1 -C 6 alkylamino group, a C 1 -C 6 alkoxycarbonyl group, an optionally substituted aryl group, or an optionally substituted heteroaryl group, two functional groups selected from the group R1, R2 and R3 and/or two functional groups selected from the group R4, R5 and R6 each being able to form, with one another and with the adjacent benzene ring, a fused aromatic or heteroaromatic five- or six-membered cycle, characterized in that at least N-[(4-methoxyphenyl)methylidene]benzenesulfonamide is contained as the sulfonimine according to formula. R1 to R6 represent, independently of one another, a hydrogen atom, a halogen atom, a C 1 -C 6 alkyl group, a partly or completely halogenated C 1 -C 6 alkyl group, a C 2 -C 6 alkenyl group, a C 1 -C 6 hydroxyalkyl group, a C 2 -C 6 polyhydroxyalkyl group, a C 1 -C 6 alkoxy group, a C 1 -C 6 alkoxy C 2 -C 6 alkyl group, an aryl C 1 -C 6 alkyl group, a hydroxy group, a nitrile group, a nitro group, a carboxylic acid group, a sulfonic acid group, a sulfonamido group, an amino group, a di C 1 -C 6 alkylamino group, a mono C 1 -C 6 alkylamino group, a C 1 -C 6 alkoxycarbonyl group, an optionally substituted aryl group, or an optionally substituted heteroaryl group, two functional groups selected from the group R1, R2 and R3 and/or two functional groups selected from the group R4, R5 and R6 each being able to form, with one another and with the adjacent benzene ring, a fused aromatic or heteroaromatic five- or six-membered cycle,