Knee prostheses featuring components that more faithfully replicate the structure and function of the human knee joint in order to provide, among other benefits: greater flexion of the knee in a more natural way by promoting or at least accommodating internal tibial rotation in a controlled way, replication of the natural screw home mechanism, and controlled articulation of the tibia and femur respective to each other in a more natural way. Surfaces can be specially shaped using iterative automated techniques that allow testing and iterative design taking into account a manageable set of major forces acting on the knee during normal functioning, together with information that is known about natural knee joint kinetics and kinematics.