An agent for oxidative hair lightening or hair coloring, containing, in each case based on the weight of the agent, - 70-90 wt.%, preferably 73-86 wt.%, particularly preferably 76-84 wt.%, water, - at least one alkalizing agent, - at least one crosslinked copolymer made up of acrylic acid and non-ethoxylated esters of acrylic acid with linear C10-C30 monoalcohols as monomers, the crosslinked copolymer being contained in a total amount of 0.2-0.6 wt.%, preferably 0.3-0.5 wt.%, particularly preferably 0.4-0.45 wt.%, in each case based on the weight of the agent, - at least one linear, saturated 1-alkanol having one hydroxy group and 8 to 22 carbon atoms in a total amount of 0.3-1.5 wt.%, preferably 0.4-1.2 wt.%, particularly preferably 0.5-1.0 wt.%, extremely preferably 0.6-0.8 wt.%, - at least one anionic surfactant in a total amount of 1-6 wt.%, preferably 2-5 wt.%, and particularly preferably 2.5-4.5 wt.%, and - at least one polymer selected from cationic and zwitterionic polymers in a total amount of 0.1-2 wt.%, preferably 0.2-1.5 wt.%, particularly preferably 0.35-0.5 wt.%, - optionally at least one coloring substance selected from oxidation dye precursors, direct hair dyes and mixtures thereof, no oxidizing agents being contained, characterized in that - sodium polyacrylate, preferably having a mass-average molar mass M W in the range of 1,000,000 to 20,000,000 daltons, particularly preferably 6,000,000 to 15,000,000 daltons, is contained, preferably in a total amount of 0.1-1.5 wt.%, particularly preferably 0.5-1.3 wt.%, extremely preferably 0.8-1.1 wt.%, in each case based on the weight of the agent, the sodium polyacrylate particularly preferably being pregelled in a water-in-oil emulsion. - 70-90 wt.%, preferably 73-86 wt.%, particularly preferably 76-84 wt.%, water, - at least one alkalizing agent, - at least one crosslinked copolymer made up of acrylic acid and non-ethoxylated esters of acrylic acid with linear C10-C30 monoalcohols as monomers, the crosslinked copolymer being contained in a total amount of 0.2-0.6 wt.%, preferably 0.3-0.5 wt.%, particularly preferably 0.4-0.45 wt.%, in each case based on the weight of the agent, - at least one linear, saturated 1-alkanol having one hydroxy group and 8 to 22 carbon atoms in a total amount of 0.3-1.5 wt.%, preferably 0.4-1.2 wt.%, particularly preferably 0.5-1.0 wt.%, extremely preferably 0.6-0.8 wt.%, - at least one anionic surfactant in a total amount of 1-6 wt.%, preferably 2-5 wt.%, and particularly preferably 2.5-4.5 wt.%, and - at least one polymer selected from cationic and zwitterionic polymers in a total amount of 0.1-2 wt.%, preferably 0.2-1.5 wt.%, particularly preferably 0.35-0.5 wt.%, - optionally at least one coloring substance selected from oxidation dye precursors, direct hair dyes and mixtures thereof, - sodium polyacrylate, preferably having a mass-average molar mass M W in the range of 1,000,000 to 20,000,000 daltons, particularly preferably 6,000,000 to 15,000,000 daltons, is contained, preferably in a total amount of 0.1-1.5 wt.%, particularly preferably 0.5-1.3 wt.%, extremely preferably 0.8-1.1 wt.%, in each case based on the weight of the agent, the sodium polyacrylate particularly preferably being pregelled in a water-in-oil emulsion. <EOS>