A device for packing cut flowers incorporating a bucket for use as a bottom part, and further incorporating a sleeve-shaped top part. The bucket incorporates a peripheral channel that is open at a top side for receiving and retaining a bottom portion of the top part, wherein the peripheral channel projects outwardly with respect to a standing wall of the bucket, and wherein the bucket incorporates a filler piece arranged underneath the peripheral channel and connecting up to both a bottom of the peripheral channel and a portion of the standing wall as present underneath the peripheral channel. Due to the presence of the filler piece on the bucket, channels of adjacent buckets being part of stacks containing buckets positioned alongside each other are prevented from meshing together.