The object of the present disclosure are agents for oxidative hair bleaching with a pH value in the range from about 10.0 to about 11.0, containing from about 70-95% by weight of water, an alkalizing agent, from about 0.1-2% by weight of anionic, zwitterionic or amphoteric surfactant, from about 0.1-1.5% by weight of sodium polyacrylate, wherein only small amounts, if any, of linear saturated alkanols having two or three hydroxy groups and from 2 to 8 carbon atoms in the alkyl group are included. Furthermore, no saturated and unsaturated non-alkoxylated alkanols having one hydroxy group and from 1 to 50 carbon atoms in the alk(en)yl group, no saturated and unsaturated alkanecarboxylic acids with 1 to 50 carbon atoms, no crosslinked copolymer built up from acrylic acid and non-ethoxylated esters of acrylic acid with linear C10-C30 monoalcohols as monomers and no oxidizing agents are contained.