A method for preparing tapered block copolymers which are particularly useful for blend components in blends with polymers of styrene. In the first embodiment of this invention the copolymers are prepared in a polymerization process by sequentially charging: (1) an initiator and monovinylaromatic monomers in the presence of a randomizer; (2) an initiator and monovinylaromatic monomers; (3) a mixture of monovinylaromatic and conjugated diene monomers; and (4) a coupling agent; to produce a polymodal tapered block copolymer. In a second embodiment of the invention tapered block copolymers are prepared in a polymerization process by sequentially charging: (1) an initiator and monovinylaromatic monomers in the presence of a randomizer; (2) an initiator and monovinylaromatic monomers; (3) a mixture of monovinylaromatic and conjugated diene monomers; (4) a mixture of monovinylaromatic and conjugated diene monomers; and (5) a coupling agent; to produce a polymodal tapered block copolymer. The invention copolymers and blends of the invention copolymers with polymers of styrene are particularly useful for applications such as packaging and food or drink containers which require transparency, low blueness, colorlessness, good impact strength and ductility.