Process for enhancing the cleaning properties of an aqueous cleaning composition comprising at least one surfactant, intended for cleaning a surface which has been soiled with soiling, by adding to said cleaning composition, at least one polymer (P) comprising: hydrophobic monomer units that are uncharged or nonionizable at the working pH of the composition of the invention and optionally at least one hydrophilic monomer unit. Preferably, the polymer employed is a copolymer containing sulfur-containing functions in the ionic form (preferably containing sulfonated or sulfated functions).