A housing for a cabinet-like household appliance has a body and at least one door, which is connected to the body in a manner that enables it to swivel due to the provision of at least one first and one second multiple-articulation hinge. The door is supported on an upper supporting surface of the first multiple-articulation hinge and on a lower supporting surface of the second multiple-articulation hinge by means of at least one shim inserted between the door and at least one of the supporting surfaces.