The present invention is a process for producing a tapered block polymer which comprises optionally anionically polymerizing styrene to form a homopolymer block of polystyrene, anionically polymerizing isoprene to form a homopolymer block of polyisoprene, and anionically copolymerizing a mixture of styrene and isoprene to form a tapered copolymer block wherein each of the monomers styrene and isoprene is introduced at a rate of 15 % to 75 % by weight of the total tapered block monomer charge per minute and the weight ratio of the styrene to the isoprene is from 0.5:1 to 1.5:1. The process produces a unique polymer containing a tapered polymer block of styrene and isoprene which has a specific taper structure consisting of small segments of variable size of styrene monomers and isoprene monomers.
