A switchable bucket tappet for a valve drive of an internal combustion engine, which has a bucket base body with a ring-shaped base guided by a skirt projecting from the outer edge of the base in a bore of the engine. A lifting cam acts on the base and a hollow cylindrical extension projects from an inner edge of the base. In the bore, an inner body is axially movable relative to the bucket base body and, formed in the underside of the inner body, is a support for indirect contact with a gas exchange valve. A coupling piston, which has a flattened portion on its upper side, runs in a bore of the inner body and is engaged with a driver surface for full valve lift. A lost motion spring acts between the bucket base body and inner body.