An apparatus for press bending glass sheets carried on a mold, the apparatus including a die having a lower surface shape to mold a glass sheet positioned thereunder to a desired curved shape, a first counterbalance assembly connected to the die for providing the die with a selected net weight, a frame mounted above the die, a plurality of flexible members connecting the die to the frame for suspending the die below the frame whereby the die is capable of unconstrained lateral and tilting movement relative to the frame and die moving device connected to the frame for vertically moving the die. The present invention also provides a method of press bending glass sheets, the method includes the steps of providing a gravity bent glass sheet carried on a gravity bending mold; lowering an upper die by a suspension system onto the glass sheet, the upper die having a lower surface to mold the glass sheet to a desired curved shape, and releasing the upper die from being supported by the suspension system so that the upper die rests on the glass sheet at a selected net weight during a press bending operation; and wherein during the lowering step the upper die is unconstrained against lateral and tilting movement so that the upper die is permitted progressively to be aligned with the bent glass sheet as the upper die comes into contact with the bent glass sheet.