Lithium-terminated polymers of one or more conjugated dienes and of one or more mono alkenyl arenes are coupled by reaction with an alkoxy silane coupling agent having the formula Rx—Si—(OR′)y, where x is 0 or 1, x+y=4, R and R′ are the same or different, R is selected from aryl hydrocarbon radicals, linear alkyl hydrocarbon radicals and branched alkyl hydrocarbon radicals, and R′ is selected from linear and branched alkyl hydrocarbon radicals, such that the resulting polymer composition contains less than about ten weight percent of uncoupled polymer diblock. The polymer compositions are subsequently selectively hydrogenated, and are useful in a variety of compounds and end use applications.