A dunnage placing apparatus includes a chassis, a dunnage magazine, and a carriage movably supported by the chassis and adapted to receive dunnage pieces from the magazine. The carriage has a lower gate, an intermediate gate substantially above the lower gate, and an upper gate substantially above the intermediate gate. The apparatus includes a control system adapted to cause dunnage pieces to be released from the magazine and received into the carriage. The control system also causes the carriage to move relative to the chassis and to release dunnage pieces. The released dunnage pieces released from the carriage can be placed at respective predetermined locations.