An effluent treatment method for treating an aqueous effluent that contains solid particles, the method including the addition to the effluent of at least one water-soluble polymer comprising at least one non-ionic monomer and at least one anionic monomer obtained by controlled radical polymerization, the said polymer having a UL viscosity of between 2 and 4.5 cps, wherein the controlled radical polymerization is a polymerization by reversible addition-fragmentation chain transfer, RAFT (Reversible Addition Fragmentation Chain Transfer Polymerization), and wherein the controlled radical polymerization is carried out with a control agent having the formula: in which - Z = O, S or N; - R1 and R2, being identical or different, represent: a group (i): alkyl, acyl, alkenyl or alkynyl, linear or crosslinked, optionally substituted; or a carbon ring (ii), either saturated or unsaturated, optionally substituted or aromatic; or a heterocycle (iii), either saturated or unsaturated, optionally substituted or aromatic, it being possible for these groups and rings (i), (ii), and (iii) to be substituted by substituted aromatic groups; or the groups: alkoxycarbonyl or aryloxycarbonyl (-COOR), carboxy (- COOH), acyloxy (-O2CR), carbamoyl (-CONR2), cyano (-CN), alkylcarbonyl, alkylarylcarbonyl, arylcarbonyl, arylalkylcarbonyl, phthalimido, maleimido, succinimido, amidino, guanidimo, hydroxy (-OH), amino (-NR2), halogen, allyl, epoxy, alkoxy (-OR), S-alkyl, S-aryl; groups that are hydrophilic or ionic in nature such as the alkali salts of carboxylic acids, the alkali salts of sulfonic acid, polyalkylene oxide chains (polyoxyethylene POE, polyoxypropylene POP), cationic substituents (quaternary ammonium salts), R representing an alkyl or aryl group. wherein the controlled radical polymerization is a polymerization by reversible addition-fragmentation chain transfer, RAFT (Reversible Addition Fragmentation Chain Transfer Polymerization), and wherein the controlled radical polymerization is carried out with a control agent having the formula: in which - Z = O, S or N; - R1 and R2, being identical or different, represent: a group (i): alkyl, acyl, alkenyl or alkynyl, linear or crosslinked, optionally substituted; or a carbon ring (ii), either saturated or unsaturated, optionally substituted or aromatic; or a heterocycle (iii), either saturated or unsaturated, optionally substituted or aromatic, it being possible for these groups and rings (i), (ii), and (iii) to be substituted by substituted aromatic groups; or the groups: alkoxycarbonyl or aryloxycarbonyl (-COOR), carboxy (- COOH), acyloxy (-O2CR), carbamoyl (-CONR2), cyano (-CN), alkylcarbonyl, alkylarylcarbonyl, arylcarbonyl, arylalkylcarbonyl, phthalimido, maleimido, succinimido, amidino, guanidimo, hydroxy (-OH), amino (-NR2), halogen, allyl, epoxy, alkoxy (-OR), S-alkyl, S-aryl; groups that are hydrophilic or ionic in nature such as the alkali salts of carboxylic acids, the alkali salts of sulfonic acid, polyalkylene oxide chains (polyoxyethylene POE, polyoxypropylene POP), cationic substituents (quaternary ammonium salts), R representing an alkyl or aryl group. - Z = O, S or N; - R1 and R2, being identical or different, represent: a group (i): alkyl, acyl, alkenyl or alkynyl, linear or crosslinked, optionally substituted; or a carbon ring (ii), either saturated or unsaturated, optionally substituted or aromatic; or a heterocycle (iii), either saturated or unsaturated, optionally substituted or aromatic, it being possible for these groups and rings (i), (ii), and (iii) to be substituted by substituted aromatic groups; or the groups: alkoxycarbonyl or aryloxycarbonyl (-COOR), carboxy (- COOH), acyloxy (-O2CR), carbamoyl (-CONR2), cyano (-CN), alkylcarbonyl, alkylarylcarbonyl, arylcarbonyl, arylalkylcarbonyl, phthalimido, maleimido, succinimido, amidino, guanidimo, hydroxy (-OH), amino (-NR2), halogen, allyl, epoxy, alkoxy (-OR), S-alkyl, S-aryl; groups that are hydrophilic or ionic in nature such as the alkali salts of carboxylic acids, the alkali salts of sulfonic acid, polyalkylene oxide chains (polyoxyethylene POE, polyoxypropylene POP), cationic substituents (quaternary ammonium salts), R representing an alkyl or aryl group. a group (i): alkyl, acyl, alkenyl or alkynyl, linear or crosslinked, optionally substituted; or a carbon ring (ii), either saturated or unsaturated, optionally substituted or aromatic; or a heterocycle (iii), either saturated or unsaturated, optionally substituted or aromatic, it being possible for these groups and rings (i), (ii), and (iii) to be substituted by substituted aromatic groups; or the groups: alkoxycarbonyl or aryloxycarbonyl (-COOR), carboxy (- COOH), acyloxy (-O2CR), carbamoyl (-CONR2), cyano (-CN), alkylcarbonyl, alkylarylcarbonyl, arylcarbonyl, arylalkylcarbonyl, phthalimido, maleimido, succinimido, amidino, guanidimo, hydroxy (-OH), amino (-NR2), halogen, allyl, epoxy, alkoxy (-OR), S-alkyl, S-aryl; groups that are hydrophilic or ionic in nature such as the alkali salts of carboxylic acids, the alkali salts of sulfonic acid, polyalkylene oxide chains (polyoxyethylene POE, polyoxypropylene POP), cationic substituents (quaternary ammonium salts), R representing an alkyl or aryl group.