Square plug in a round hole for hole enlargement

To enlarge existing holes, especially large ones made with a Forstner bit or holesaw, you can't just plug them with a dowel and then redrill. Last time I found myself in this spot, I realized that the filler plug didn't necessarily have to be round. A block of scrapwood does nicely.

Size the block for a snug fit in the hole, then mark the center of the block by drawing lines from corner to corner. X marks the spot for drilling the larger hole because the center mark of the block is also the hole center mark.
—Mike Randall, Ohia, Southland, New Zealand