Golf balls having a core including a material formed from a controlled-isomer polybutadiene, a crosslinking agent, and a free-radical initiator, or a reaction product thereof, and a cover having a plurality of dimples disposed about the core, wherein the controlled-isomer polybutadiene includes at least about 10 percent to 80 percent trans-isomer and no more than about 5 percent vinyl-configuration polybutadiene and wherein the controlled-isomer polybutadiene has both an absolute molecular weight of at least about 250,000 and a polydispersity of no more than about 3 prior to crosslinking. In particular, golf balls having a compression below about 80 without significant loss of resilience can be advantageously prepared with such materials. Methods of preparing such golf balls are also recited.