Semifinished products or leather are or is produced by a process in which pelts, pickled pelts or semifinished products are treated with a) at least one sheet silicate and b) at least one copolymer which is obtainable by copolymerization of at least one ethylenically unsaturated dicarboxylic anhydride (A), derived from at least one dicarboxylic acid of 4 to 8 carbon atoms, at least one vinylaromatic compound (B1) or at least one oligomer (B2) of branched or straight-chain C2-C10-alkene, at least one oligomer having an average molecular weight Mn of from 300 to 5 000 g/mol or being obtainable by oligomerization of at least 3 equivalents of C2-C10-alkene, and optionally at least one ethylenically unsaturated monomer (C) differing from (A) and having at least one hetero atom, and reaction with at least one compound (D) of the formula I a or I b and optionally hydrolysis with water or aqueous alkaline solution, where, in formula I a and I b, A1 are identical or different and are C2-C6-alkylene R1 is linear or branched C1-C20-alkyl and n is an integer from 1 to 200.