Process for preparing water-absorbing polymers, comprising the process steps of ( i) mixing (α1) 0.1 to 99.999% by weight, preferably 20 to 98.99% by weight and more preferably 30 to 98.95% by weight of polymerizable, ethylenically unsaturated monomers containing acid groups, namely acrylic acid or salts thereof or mixtures thereof, (α2) 0 to 70% by weight, preferably 1 to 60% by weight and more preferably 1 to 40% by weight of polymerizable, ethylenically unsaturated monomers copolymerizable with (α1), (α3) 0.001 to 10% by weight, preferably 0.01 to 7% by weight and more preferably 0.05 to 5% by weight of one or more crosslinkers, (α4) 0 to 30% by weight, preferably 1 to 20% by weight and more preferably 5 to 10% by weight of water-soluble polymers, (α5) 0-90% by weight, preferably 2.5-75% by weight and more preferably 10-60% by weight of water, and (α6) 0-20% by weight, preferably 0-10% by weight and more preferably 0.1-8% by weight of one or more assistants, where the sum of the weights of (α1) to (α6) is 100% by weight, (ii) free-radical polymerization with crosslinking to form a water-insoluble, aqueous untreated hydrogel polymer, (iii) comminuting the hydrogel polymer, (iv) drying the hydrogel polymer, (v) grinding and sieving the hydrogel polymer to size, (vi) surface postcrosslinking the ground and sieved hydrogel polymer and (vii) finishing the water-absorbing polymer, wherein the water-absorbing polymer has been treated with 0.0001 to 3% by weight, preferably 0.002 to 2% by weight and more preferably 0.007 to 1.8% by weight of a peroxo compound, based on the acrylic acid, after the polymerization, wherein the peroxo compound is added in steps (iii) to (vii) and wherein the peroxo compound is potassium peroxomonosulphate triple salt. ( i) mixing (α1) 0.1 to 99.999% by weight, preferably 20 to 98.99% by weight and more preferably 30 to 98.95% by weight of polymerizable, ethylenically unsaturated monomers containing acid groups, namely acrylic acid or salts thereof or mixtures thereof, (α2) 0 to 70% by weight, preferably 1 to 60% by weight and more preferably 1 to 40% by weight of polymerizable, ethylenically unsaturated monomers copolymerizable with (α1), (α3) 0.001 to 10% by weight, preferably 0.01 to 7% by weight and more preferably 0.05 to 5% by weight of one or more crosslinkers, (α4) 0 to 30% by weight, preferably 1 to 20% by weight and more preferably 5 to 10% by weight of water-soluble polymers, (α5) 0-90% by weight, preferably 2.5-75% by weight and more preferably 10-60% by weight of water, and (α6) 0-20% by weight, preferably 0-10% by weight and more preferably 0.1-8% by weight of one or more assistants, where the sum of the weights of (α1) to (α6) is 100% by weight, (α1) 0.1 to 99.999% by weight, preferably 20 to 98.99% by weight and more preferably 30 to 98.95% by weight of polymerizable, ethylenically unsaturated monomers containing acid groups, namely acrylic acid or salts thereof or mixtures thereof, (α2) 0 to 70% by weight, preferably 1 to 60% by weight and more preferably 1 to 40% by weight of polymerizable, ethylenically unsaturated monomers copolymerizable with (α1), (α3) 0.001 to 10% by weight, preferably 0.01 to 7% by weight and more preferably 0.05 to 5% by weight of one or more crosslinkers, (α4) 0 to 30% by weight, preferably 1 to 20% by weight and more preferably 5 to 10% by weight of water-soluble polymers, (α5) 0-90% by weight, preferably 2.5-75% by weight and more preferably 10-60% by weight of water, and (α6) 0-20% by weight, preferably 0-10% by weight and more preferably 0.1-8% by weight of one or more assistants, where the sum of the weights of (α1) to (α6) is 100% by weight, (ii) free-radical polymerization with crosslinking to form a water-insoluble, aqueous untreated hydrogel polymer, (iii) comminuting the hydrogel polymer, (iv) drying the hydrogel polymer, (v) grinding and sieving the hydrogel polymer to size, (vi) surface postcrosslinking the ground and sieved hydrogel polymer and (vii) finishing the water-absorbing polymer,