A device for compressing tires and other compressible items in a shipping container comprises a support frame 22 attached to the lift end of a forklift. A fixture 20 is attached to and moves vertically with the support frame. The fixture comprises a horizontal compression platen 30. A vertical pusher plate 50 extends above and below the platen. The upper pusher plate 53, which is above the platen, can fold down so that the platen can be brought near the ceiling of a shipping container above a stack of tires. The fixture weighs enough to compress tires stacked below the compression platen. Additional tires are stacked above the platen and compressed tires. The upper pusher plate is then folded up, against the tires. Two hydraulic cylinders push the pusher plate away from the support frame to pull the platen from between the tires.