A process for making a coupled block copolymer, comprising the steps of: a) reacting a living lithium-terminated polymer having the formula P-Li, where P is a copolymer chain of the structure A-B- or A-B-B', wherein the block A represents a block of mono alkenyl arenes having 8 to 18 carbon atoms, wherein the block B and block B' represents a poly conjugated diene block, a copolymer block of conjugated dienes, a copolymer block of a conjugated diene and a mono alkenyl substituted arene, in which case the total content of mono alkenyl-substituted arene may be up to 70 weight percent, or a combination of such blocks, and wherein the block B or the block B' is attached to the coupling agent, wherein the one or more conjugated dienes have 4 to 12 carbon atoms and P has a number average molecular weight of from 25,000 to 200,000, with an alkoxy silane coupling agent having the formula Si 4, where R is selected from linear and branched alkyl radicals, and wherein the molar ratio of Si to Li is between 0.4 and 0.55, thereby forming a coupled block copolymer composition, comprising: (i) a tetra-branched block copolymer represented by the general formula 4 X; (ii) a tri-branched block copolymer represented by the general formula 3 X; (iii) a di-branched block copolymer represented by the general formula 2 X; and a linear block copolymer represented by the general formula P; wherein X represents the residue of said alkoxy silane coupling agent, and wherein the relative amounts of copolymers I, II, III and IV are 0 to 5 weight percent IV, 0 to 60 weight percent III, 40 to 95 weight percent II and 2 to 10 weight percent I, wherein the total of I, II, III and IV equals 100 weight percent. b) hydrogenating the coupled block copolymer composition by a hydrogenation process; and c) recovering the resulting block copolymer composition. a) reacting a living lithium-terminated polymer having the formula P-Li, where P is a copolymer chain of the structure A-B- or A-B-B', wherein the block A represents a block of mono alkenyl arenes having 8 to 18 carbon atoms, wherein the block B and block B' represents a poly conjugated diene block, a copolymer block of conjugated dienes, a copolymer block of a conjugated diene and a mono alkenyl substituted arene, in which case the total content of mono alkenyl-substituted arene may be up to 70 weight percent, or a combination of such blocks, and wherein the block B or the block B' is attached to the coupling agent, wherein the one or more conjugated dienes have 4 to 12 carbon atoms and P has a number average molecular weight of from 25,000 to 200,000, with an alkoxy silane coupling agent having the formula Si 4, where R is selected from linear and branched alkyl radicals, and wherein the molar ratio of Si to Li is between 0.4 and 0.55, thereby forming a coupled block copolymer composition, comprising: (i) a tetra-branched block copolymer represented by the general formula 4 X; (ii) a tri-branched block copolymer represented by the general formula 3 X; (iii) a di-branched block copolymer represented by the general formula 2 X; and a linear block copolymer represented by the general formula P; wherein X represents the residue of said alkoxy silane coupling agent, and wherein the relative amounts of copolymers I, II, III and IV are 0 to 5 weight percent IV, 0 to 60 weight percent III, 40 to 95 weight percent II and 2 to 10 weight percent I, wherein the total of I, II, III and IV equals 100 weight percent. (i) a tetra-branched block copolymer represented by the general formula 4 X; (ii) a tri-branched block copolymer represented by the general formula 3 X; (iii) a di-branched block copolymer represented by the general formula 2 X; and a linear block copolymer represented by the general formula P; wherein X represents the residue of said alkoxy silane coupling agent, and wherein the relative amounts of copolymers I, II, III and IV are 0 to 5 weight percent IV, 0 to 60 weight percent III, 40 to 95 weight percent II and 2 to 10 weight percent I, wherein the total of I, II, III and IV equals 100 weight percent. b) hydrogenating the coupled block copolymer composition by a hydrogenation process; and c) recovering the resulting block copolymer composition.