Disclosed herein is a multi-layer golf ball having a soft outer cover. The golf ball has an inner cover layer with a Shore D hardness of 60 or more, and an outer cover with a Shore D hardness of 55 or less, and more preferably 50 or less. In a particularly preferred form of the invention, the outer cover comprises at least 75% of a soft copolymer formed from a polyolefin, an unsaturated carboxylic acid, and a monomer of the acrylate ester class. The golf ball of the invention has exceptionally soft feel and high spin rates on short shots of 80 yards or less and, particularly, 40 yards or less, while maintaining good distance and average spin on full shots.