A headrest assembly securable to a motor-vehicle seat back part has a movable headrest and a rod fixed in the seat back and having a plurality of vertically spaced catch formations. A spring carried on the headrest has a pair of legs flanking the rod, elastically deflectable toward and away from the rod, and biased elastically toward the rod, and a crosspiece connecting the legs and fittable with one of the catch formations. An actuator shiftable in the slide relative to the spring has respective actuating formations engageable with the spring legs. The actuator is movable between a latching position in which the actuating formations are generally disengaged from the respective legs and the crosspiece engages the rod and an unlatching position in which the actuating formations engage the respective legs and press them into the released position.