The invention describes a process for producing a diene polymer, the process comprising the following steps in this order: i) polymerizing one or more diene monomers in the presence of a catalyst composition to give a reaction mixture; ii) adding to the reaction mixture one or more alkoxysilane compounds; iii) adding S2Cl2, SCl2, SOCl2, S2Br2, SOBr2 or a mixture thereof to the reaction mixture; and iv) optionally adding a protic agent to the reaction mixture so as to deactivate the catalyst. The invention further includes polymers that are obtainable according to this process, as well as products including the polymer.