Abstract: A method for treating a suspension of mineral particles in water, such as mineral tailings, includes the step of contacting the suspension of mineral particles in water with a specific water-soluble polymer. This polymer is preferably a water-soluble polymer having an anionicity of between 10 to 55 mol %, and more preferably 20 to 50 mol %. Furthermore, this polymer has preferably a molecular weight between 15 and 40 million daltons, and more preferably between 18 and 30 million. The method involves adding the specific polymer into a thickener containing the tailings to treat, and/or during transport of the suspension to a deposition area for dewatering and solidification, or to the tailings to treat followed by a mechanical treatment such as centrifugation, screw press and filtration.