Deep drawing tool (10) and process for deep drawing blanks (32), which are punched out of sheet metal that is painted or coated with film material, in order to obtain flangeless formed pieces, the deep drawing tool (10) comprising a drawing bell (12), a drawing core (14), a blank holder (18), and a die cushion for applying a spring force to the blank holder (18) using force transmission means (20, 22), characterized by a drive unit which, once the drawing bell (12) has reached a predefined position in its downward movement, drives the force transmission means (20, 22) to perform a movement preceding the movement of the drawing bell (12).