A leveling device assists in support of stackable objects having a non-uniform thickness, such as DocuCards, in a stackable tray. The stackable tray includes a pivoting tray that can be pivoted from a full sheet stack position to an empty sheet stack position. A valley removal mechanism is provided on the pivoting tray to variably support an intermediate portion of the bottom of the stack to compensate for and remove a valley created intermediate ends of the stack due to an aggregate effect of stack media of non-uniform thickness. The valley removal mechanism preferably includes a support surface that contacts a bottom of the stack, a ramp defining a ramp profile, and a ramp follower that guides the support surface to a variable orientation that compensates for the valley as the stack height changes.