A construction for a shoe, particularly an athletic shoe such as a running shoe, includes a sole that is constructed according to the applicant's prior invention of a theoretically ideal stability plane. Such a shoe sole according to that prior invention conforms to the natural shape of the foot, particularly the sides, and that has a constant thickness in frontal plane cross sections; the thickness of the shoe sole sides contour equals and therefore varies exactly as the thickness of the load-bearing sole portion. The new invention relates to the use of the theoretically ideal stability plane concept to provide natural stability in negative heel shoe soles that are less thick in the heel area than in the rest of the shoe sole. This new invention also relates to the use of the theoretically ideal stability plane concept to provide natural stability in flat shoe soles that have no heel lift, maintaining the same thickness throughout; such a design avoids excessive structural rigidity by using contoured stability sides abbreviated to only essential structural support elements to provide the shoe sole with natural flexibility paralleling that of the human foot. The abbreviation of essential structural support elements can also be applied to negative heel shoe soles, again to avoid excessive rigidity and to provide natural flexibility.