An elevator safety based on having the elevator lift-rod, under the influence of the elevator governor, cause to rotate approximately elliptical cams, called quasi-elliptical cams. The cams are wider in one orientation, just as an ellipse has a major axis, wider than its minor axis. The cams are positioned to push against a brake pad as they rotate so that the major axis of each cam changes orientation with the minor axis. The cams can be shaped to simulate a wedge-type safety, even one using a wedge with multiple ramp angles. With essentially no additional complexity, the cam safety can be designed to operate with a bi-directional governor, one which exerts, usually through an intermediate linkage, force on the lift-rod in either the up or down motion depending on the unintended motion of the elevator.