Described herein is a structure of a motor-vehicle door including a multi-thickness metal sheet pressed and shaped to define: a hinge area configured for fastening one or more hinges for connection to the body of a motor vehicle; a panel area configured for receiving an upholstery-trim element for the door; and a frame area configured for receiving a window of the door. The above multi-thickness metal sheet has a first thickness in said hinge area, a second thickness in said panel area, and a third thickness in said frame area.