An apparatus for closing a flap on an open end of a box may include a device having a slot and a mechanism operable to provide a relative motion between the slot and the flap. The relative motion may cause the flap to be received into the slot and the flap to be reoriented to a closed position. A method of closing an open end of a box being conveyed downstream, with the open end facing transversely, may include two operations. With a trailing minor flap on the open end being held in a substantially upstream-pointing open position, the opposing leading minor flap on the open end may be closed from a substantially downstream-pointing open position to a substantially upstream-pointing closed position. With the leading minor flap being held in the closed position, the trailing minor flap may be closed from the open position to a substantially downstream-pointing closed position.