Methods of producing vinyllactam copolymers which include: providing at least one water-soluble N-vinyllactam; providing at least one hydrophobic comonomer; and subjecting the at least one water-soluble N-vinyllactam and the at least one hydrophobic comonomer to free-radical polymerization in an organic solvent in the presence of an initiator, under a combination of process measures selected from the group consisting of A and B; wherein: (A) comprises (i) polymerization under reflux, and at least two of (ii), (iii), (iv), (v), (vi), and (vii), wherein (ii) comprises an addition of at least 5 mol % of N-vinyllactam to the polymerization mixture if at least 70 mol % of the total amount of hydrophobic monomer used have completely reacted, (iii) comprises return of condensate formed in the reflux from below to the polymerization mixture, (iv) comprises introduction of the initiator in the form of a solution in an organic solvent from below into the polymerization mixture, (v) comprises addition of N-vinyllactam to the reflux, (vi) comprises distilling off a portion of the organic solvent and continuing the polymerization following conversion of 70 to 99% by weight of the N-vinyllactam used, and (vii) comprises introduction of at least one monomer from below into the polymerization mixture; and wherein (B) comprises (viii) polymerization under a superatmospheric pressure such that vaporization of the polymerization components is avoided, and at least one of (i), (ii), (iii), (iv), (v), (vi), and (vii), with the proviso that a combination of (viii) with any of (i), (iii) or (v) is carried out sequentially.