The present invention is directed to an improved golf ball displaying the desired spin profile and having a generally rigid, thermoset polybutadiene outer core surrounding a relatively soft, low compression inner core. In general, this golf ball has an inner core and at least one outer core layer surrounding the inner core. The inner core has a hardness less than a hardness of the outer core and a specific gravity less than or equal to the outer core specific gravity. Overall the inner core compression and outer core are formulated to provide a combined overall core compression of greater than about 50, preferably greater than about 70. A cover layer is provided to surround and to cover the outer core layer. A moisture barrier layer is provided between the outer core layer and the cover layer to protect the inner and outer cores from degradation due to exposure to water. The moisture vapor transmission rate of the moisture barrier layer is selected to be less than the moisture vapor transmission rate of the cover layer.