A golf ball includes a core made from a highly neutralized polymer that has been mixed with a hardness modifier. The modifier may be a process oil or a plasticizer. In particular, the modifier may be a naphthenic process oil, a paraffinic process oil, a phthalate plasticizer, a trimellitate plasticizer, an adipate plasticizer, a sebacate-based plasticizer, a maleate-based plasticizer, and blends thereof. Also disclosed is a method for manufacturing a golf ball that includes changing the hardness of a highly neutralized polymer core.