A golf ball comprising a core comprised of a polymer containing an acid group fully-neutralized by an organic acid or a salt, a cation source, or a suitable base thereof, the core having a first Shore D hardness, a compression of no greater than about 90, and a diameter of between about 1.00 inches and about 1.64 inches; and a cover layer comprising ionomeric copolymers and terpolymers, ionomer precursors, thermoplastics, thermoplastic elastomers, polybutadiene rubber, balata, grafted metallocene-catalyzed polymers, non-grafted metallocene-catalyzed polymers, single-site polymers, high-crystalline acid polymers and their ionomers, or cationic ionomers.