Golf balls having a multi-layer core and a cover are disclosed. The multi-layer core contains a center and an outer core layer that are both soft relative to a hard intermediate core layer. The outer core layer is thin relative to the center and outer core layer. In one embodiment, the relatively hard intermediate core layer has a surface hardness of 80 to 90 Shore C which is greater than the center hardness and surface hardness of the outer core layer. In another embodiment, the cover includes an inner cover layer having a surface hardness of 60 Shore D or greater and an outer cover layer having a surface hardness of 20 to 70 Shore D.