The present invention provides monopolar acetabular liners that can enclose a femoral head to form a hip replacement prosthesis, wherein the liner has a rim that creates an orifice, wherein the orifice has a diameter that is smaller than the diameter of the femoral head, and wherein the liner encompasses greater than 50 percent of the volume of the head, wherein a constraining ring can be used in conjunction with the monopolar constrained acetabular liner to provide additional support for the femoral head to stay with the acetabular liner and avoid dislocation. Assemblies, complete prosthetic replacements, and methods of replacing also are provided. Liners and constraining rings having no, one or more recesses also are provided.