Tire rubbers which are prepared by anionic polymerization are frequently coupled with a suitable coupling agent, such as a tin halide, to improve desired properties. It has been unexpectedly found that greatly improved properties for tire rubbers, such as lower hysteresis, can be attained by asymmetrically coupling the rubber. This invention more specifically discloses an asymmetrical tin-coupled rubbery polymer which is particularly valuable for use in manufacturing tire tread compounds, said asymmetrical tin-coupled rubbery polymer being comprised of a tin atom having at least three polydiene arms covalently bonded thereto, wherein at least one of said polydiene arms has a number average molecular weight of less than about 40,000, wherein at least one of said polydiene arms has a number average molecular weight of at least about 80,000, and wherein the ratio of the weight average molecular weight to the number average molecular weight of the asymmetrical tin-coupled rubbery polymer is within the range of about 2 to about 2.5.