A prosthetic joint includes: (a) a first member comprising rigid material including a wear-resistant, concave cup surface; and (b) a second member comprising rigid material with a wear-resistant, convex contact surface; (c) one of the surfaces includes: (i) an annular first flange defining a protruding wear-resistant first contact rim at or near an apex of the member; and (ii) an annular second flange defining a protruding wear-resistant second contact rim, at or near an outer periphery of the member; (d) the first and second contact rims bear directly against the contact surface, so as to transfer loads between the first and second members, while allowing pivoting motion therebetween; and (e) the flanges are shaped and sized so as to deform elastically and permit the contact rims to conform in an irregular shape to the surface of the opposite member, when the joint is placed under a predetermined load.