Cut twice for a perfectly centered mortise

Recently, I built a futon using mortise and tenon joinery. However, when I cut the first mortises, I had a slight problem getting them centered perfectly. When assembling the leg to the rail, it required some sanding to get the joints flush. I solved the problem by drilling the overlapping holes twice. After the first drilling operation, I turned the work-piece around to put the other face against the drill press fence. During the redrilling, the bit just shaved the other side of the mortise, leaving an equal reveal on both sides. Once I had the mortises cut and cleaned, I cut the tenons to fit the mortises and had very little trouble getting the joints to fit flush.
—Ernie Dennis, Goshen, N.H.