A multi-part cooled piston for an internal combustion engine comprises a one-piece piston upper part having a combustion bowl and an annular wall with a piston-ring part, and a one-piece piston lower part having a box-like piston skirt, and bosses to receive the piston pins joining the piston to the connecting rod and boss supports, which are joined to the piston skirt. A cooling channel is formed through the piston upper part and also the piston lower part and is limited thereby in its cross section. A reduction of the compression height and an increase of the heat load can be achieved with this piston despite increasing engine power. The piston can also be assembled without microstructural change. The piston upper part and the piston lower part are provided with support elements having seating faces, which form a first and a second seat. The support element comprising the first seat is provided with threads for screwing the two piston parts together, and in the screwed together condition of the piston upper part and piston lower part, the two piston parts are braced exclusively via the first and second seats.