A surgical stapler having an end effector with a reduced stacking height for its components to decrease the diameter of a trocar cannula or other access device during minimally invasive surgery is disclosed. The end effector includes an elongated channel containing a staple cartridge and an anvil movable toward and away from the channel. The anvil is movable to first, second and third fixed positions relative to the channel. The first fixed position is a closed position which eliminates clearance between the anvil and cartridge. The second fixed position is an open position for inserting tissue between the anvil and cartridge. The third fixed position is a clamped position where a tissue-clamping gap exists between the anvil and cartridge to properly clamp tissue. The elimination of clearance between the anvil and cartridge of the first fixed position of the anvil reduces the stacking height, and therefore enables the user to insert the stapler through a smaller diameter access opening.