Composition comprising one or more polymers and one or more substances selected from telomers having a number average degree of telomerization of less than or equal to 8.0 (substances A) and optionally from substances such as diesters of phthalic acid or diesters of saturated aliphatic ,-dicarboxylic acids (substances B), the weight of substance(s) A plus substance(s) B together relative to the weight of the composition being greater than 20%, on the one hand, and the weight of substance(s) A relative to the weight of substance(s) A plus substance(s) B together being greater than 20%, on the other hand. Articles or parts of articles manufactured using this composition.