A method for preparing a comb copolymer, of which the backbone consists, for 0% molar: - Of 50% to 100% molar of monomeric units from 2-acrylamido-2-methyl-propanesulphonic acid, and up to 50% of optional backbone monomeric units, on which lateral poly(N-alkyl acrylamide) or poly(N,N-dialkyl acrylamide) segments are grafted, said method comprising the following successive steps: -A step (a) of reacting a compound of formula (II): CH
2 =C(R2)-C(=O)-N(R3)(R4) (II), with a chain-limiting compound of formula (IIIa): HS-R1-NH2 (IIIa) or of formula (IIIb): HS-R1-C(=O)-OH (IIIb), in order to obtain a poly(N-alkyl acrylamide) or poly(N,N-dialkyl acrylamide) telomer, of formula (Ia): H2N-R1-S-{CH2-C(R2)[C(=O)N(R3)(R4)]-}n-H (Ia) or of formula (Ib): HO-C(=O)-R1-S-{CH2-C(R2)[C(=O)N(R3)(R4)]-}n-H (Ib) formula (IIIa) or (IIIb) in which n represents a whole number greater than or equal to 2 and less than or equal to 100; -A step (c) of reacting the telomer of formula (Ia) or of formula (Ib) in tert-butanol with glycidyl methacrylate (IV) to obtain a solution of the macromonomer of formula (Va): CH2=C(R5)-C(=O)-NH-R1-Z-{CH2-C(R2)[C(=O)N(R3)(R4)]-}n-H (Va) or of formula (Vb); CH2=C(R5)-C(=O)-O-(C=O)-R1-Z-{CH2-C(R2)[C(=O)N(R3)(R4)]-}n-H (Vb); -A step (e) of copolymerising the macromonomer of formula (Va) or of formula (Vb) in tert-butanol with the ammonium salt of 2-acrylamido-2-methyl-propanesulphonic acid, and, if applicable, with the optional monomer or monomers in the desired molar proportions; novel comb copolymers.