The invention relates to the use of a weakly ionic and water-soluble copolymer as a grinding aid agent for grinding mineral matter in aqueous suspension in order to obtain aqueous suspensions of refined mineral matter, with a dry matter concentration that can be high, with a low Brookfield.TM. viscosity that remains stable over time, having the property that it presents a pigmentary surface area the ionic charge of which, as determined by ionic titration, is low. The invention relates to the aqueous suspensions of mineral matter obtained and their use in the fields of paper, paint and plastics.