A method of implanting an intervertebral implant or component thereof, in which each component is selected to have an inner surface and an outer surface which engages an adjacent vertebra and presents only three distinct points of contact with a cortical rim of the vertebra. The outer surface is selected to have a footprint which is sized to be within that of the cortical rim. In disclosed embodiments, the footprint can be convexo-concave shaped or kidney shaped. The intervertebral implant can be provided with upper and lower (or first and second) components which engage adjacent first and second vertebrae and which move relative to one another. The implant has both the first and second outer surfaces sized to present a respective footprint sufficient for two lateral-anterior and one posterior points of contact with an adjacent cortical rim of the respective first and second vertebra.