A headrest for a motor vehicle seat, said headrest comprising: • a frame for mounting on a backrest of said seat, said frame comprising two parallel vertically extending rods, • a main body slidably mounted on said rods so as to be able to adopt a plurality of vertical adjustment positions, • a first device for locking said main body in the selected adjustment position, • a secondary body slidably mounted longitudinally on said main body, so that said secondary body can adopt a plurality of longitudinal adjustment positions, • a second device for locking said secondary body in the selected adjustment position, said device comprising a latch mounted for vertical sliding on said main body between a locking position, in which it cooperates with a locking rack extending longitudinally on said secondary body, and an unlocking position, in which it moves away from said rack to release sliding of said secondary body, • a common cross-member for unlocking said devices, said cross-member being transversely slidably mounted on said main body, said cross-member having an end provided with a button enabling it to be actuated for unlocking, so as to release the sliding of said main and secondary bodies, • spring means for returning said crosspiece to the locked position, said headrest being characterized in that: • said crosspiece is provided with an actuating rack, • a pinion is rotatably mounted on said main body along a longitudinal axis, said pinion meshing with said actuating rack, said pinion being provided with a first and a second eccentric, • said latch is provided with a window having an upper edge and a lower edge, said eccentrics being positioned so that: o said first eccentric rests against said lower edge when said crosspiece is in the locking position, so as to block said latch in the locking position, o said second eccentric bears against said upper edge when said crosspiece is actuated to unlock, so as to spread said latch to bring it into the unlocked position. • a frame for mounting on a backrest of said seat, said frame comprising two parallel vertically extending rods, • a main body slidably mounted on said rods so as to be able to adopt a plurality of vertical adjustment positions, • a first device for locking said main body in the selected adjustment position, • a secondary body slidably mounted longitudinally on said main body, so that said secondary body can adopt a plurality of longitudinal adjustment positions, • a second device for locking said secondary body in the selected adjustment position, said device comprising a latch mounted for vertical sliding on said main body between a locking position, in which it cooperates with a locking rack extending longitudinally on said secondary body, and an unlocking position, in which it moves away from said rack to release sliding of said secondary body, • a common cross-member for unlocking said devices, said cross-member being transversely slidably mounted on said main body, said cross-member having an end provided with a button enabling it to be actuated for unlocking, so as to release the sliding of said main and secondary bodies, • spring means for returning said crosspiece to the locked position, • said crosspiece is provided with an actuating rack, • a pinion is rotatably mounted on said main body along a longitudinal axis, said pinion meshing with said actuating rack, said pinion being provided with a first and a second eccentric, • said latch is provided with a window having an upper edge and a lower edge, said eccentrics being positioned so that: o said first eccentric rests against said lower edge when said crosspiece is in the locking position, so as to block said latch in the locking position, o said second eccentric bears against said upper edge when said crosspiece is actuated to unlock, so as to spread said latch to bring it into the unlocked position. o said first eccentric rests against said lower edge when said crosspiece is in the locking position, so as to block said latch in the locking position, o said second eccentric bears against said upper edge when said crosspiece is actuated to unlock, so as to spread said latch to bring it into the unlocked position.