Disclosed herein is a hard disk drive slider having an extended three-dimensional air-bearing surface (ABS). The slider has an ABS and a back surface opposite the ABS, where at least a portion of the back surface defines a plane (i.e., if the back surface is substantially flat, the back surface itself defines the plane). Defined herein is an ABS function, which describes the characteristics of a portion of the ABS in a two-dimensional plane made by taking a cross-section of the slider perpendicular to the plane defined by the at least a portion of the back surface. The cross-section of the slider taken perpendicular to the plane has an ABS function that is a multi-valued function, which is defined herein as a relation for which, for at least one possible input value along the selected axis in the plane, the relation evaluates to two or more distinct nonzero values.