A method for placing a prosthetic acetabular cup within an acetabulum comprises implanting an acetabular cup with an eccentric socket. The acetabular cup may be substantially hemispherical with a cup rim and a portion of the cup rim removed defining a relief. The cup may accommodate a concentric liner in an eccentric position. Screw apertures may be present on the periphery of the cup and the screw trajectories may converge toward the dome of the cup. The cup is attached to a tool which is offset relative to the cup because of the substantially eccentric socket. The relief, when the cup is secured to the acetabulum, is positioned substantially anterior and the socket is positioned more posterior to provide a more natural center of rotation of a femoral head within the socket. The first relief reduces impingement of the acetabular cup on soft tissue.