An associative thickening copolymer, water-soluble in a neutral or alkaline medium, for charged and/or pigmented, white or colored aqueous compositions is disclosed. The copolymer is composed of (a) at least one monomer with ethylenic unsaturation having at least one carboxylic function, (b) at least one other monomer with ethylenic unsaturation without a carboxylic function, (c) at least one surfactant monomer having at least one urethane function resulting from the reaction of an isocyanate with ethylenic unsaturation with a surfactant compound having a hydroxyl function which is reactive with regard to the --NCO group, wherein said copolymer belongs to the group composed of those which, by definition, placed in aqueous solution with 2% by weight of dry material, brought to a pH of 9 by the addition of ammonia and at a temperature of 20.degree. C., have a Brookfield viscosity at 100 revolutions per minute of at most equal to 220 centipoises.The copolymer may be is used in charged and/or pigmented aqueous compositions such as coating compositions and, more particularly, coating colors, printing pastes, leather finishing products, cosmetic and detergent compositions and drilling fluids.