The vulcanizable rubber mixture according to this invention is used for rubber products in particular vehicle tires and vehicle tire treads, but also technical rubber products like belts on conveyor systems, technical hoses, vibration dampers and impact dampers, or wire coatings. All these products benefit from the improved processability that is achieved with the invention in that the mixture comprises a polymer represented by the formula F1-A-F2, or a mixture of F1-A-F2 with an astral or radial coupling product of F1-A-units, coupled by a multivalent coupling agent; wherein F1 represents a terminal functionalization of the polymeric chain, F2 represents a terminal functionalization different from F1; and A represents the polymeric chain of a polymer formed by the copolymerization between one or more conjugated dienes with one or more aromatic vinyl monomers.