A golf ball comprising a core and a cover layer, wherein the cover layer provides one or more deep depressions that extend through the cover layer to and/or into a layer or component underneath is disclosed. The cover may be a single layer or it may include multiple layers. If the cover is a multi-layer cover, the deep depressions extend to or into at least the first inner cover layer, and may extend to and/or into two or more inner cover layers. If the cover is a single layer, the deep depressions extend to and/or into the core. The cover layer(s) may be formed from any material suitable for use as a cover, including, but not limited to, ionomers, non-ionomers and blends of ionomers and non-ionomers. The deep depressions may be spherical or non-spherical, and the portion of the deep depression that extends to or into the next inner layer may be the same or different shape as the outer portion of the deep depression.