It has been unexpectedly found that certain neodymium catalyst systems can be used to copolymerize isoprene and 1,3-butadiene to produce random isoprene-butadiene copolymer rubbers which are not tapered. These random isoprene-butadiene copolymer rubbers have properties which are beneficial for use in rubber formulations for manufacturing a wide variety of rubber products, such as tires, hoses, conveyor belts, power transmission belts, and shoe soles. These random isoprene-butadiene rubbers are synthesized by copolymerizing (a) isoprene monomer or a substituted isoprene monomer and (b) 1,3-butadiene monomer in the presence of a neodymium catalyst system, wherein the neodymium catalyst system is prepared by (1) reacting a neodymium carboxylate with an organoaluminum compound in the presence of a conjugated diolefin monomer to produce neodymium-aluminum catalyst component, and (2) subsequently reacting the neodymium-aluminum catalyst component with an alkyl aluminum chloride to produce the neodymium catalyst system.