A safety joint for use in a subterranean well can include separable portions which, when separated, disconnect sections of a tubular string. Elongation of the safety joint can be permitted while longitudinal compression of the safety joint is prevented. A method of activating a safety joint in a subterranean well can include providing the safety joint with portions having end connectors which interconnect the safety joint between sections of a tubular string, permitting elongation of the safety joint, thereby facilitating disconnection of the tubular string sections, and then preventing longitudinal compression of the safety joint. Another safety joint can include separable portions, and a locking device which permits relative displacement between a generally tubular mandrel and a component of the safety joint in one direction, and prevents relative displacement between the mandrel and the component in an opposite direction.