The present invention is directed to a multi-layer golf ball comprising at least one core or core layer, at least one intermediate layer, and at least one cover layer. The core has a diameter of about 1.20 to about 1.56 in. and a PGA compression of about 40 to about 90. The intermediate layer comprises a modified ionomeric polymer, and it has a thickness of about 0.01 to about 0.10 in. and a Shore D hardness of about 30 to about 70. The cover layer has a Shore D hardness of about 40 to about 75. The multi-layer golf balls of the present invention provide high driver ball speed and/or a high Coefficient of Restitution, while maintaining excellent shot feel.