A golf ball comprising a core and a cover, wherein the core consists of: a solid inner core layer formed from a plasticized non-acid polymer composition PCp/N-A and having a diameter of 1.10 inch or less and a center Shore C hardness (Hcenter) of 50 or less, one or more optional intermediate core layers, and an outer core layer formed from at least one of a thermoset rubber composition TR and a thermoplastic composition TP and having a thickness of 0.200 inches or greater and an outer surface Shore C hardness (Houter surface) of 70 or greater, wherein Houter surface>Hcenter, and Houter surface−Hcenter≧40. In another embodiment, the center Shore C hardness (Hcenter) is 40 or less, the outer surface Shore C hardness (Houter surface) is 85 or greater, and Houter surface−Hcenter≧45. In one embodiment, an intermediate layer is disposed between the outer core layer and the cover. The plasticized non-acid polymer composition PCp/N-A. may be formed from at least one non-acid polymer composition and at least one plasticizer.