Bleeding may occur at the proximal anastomosis of an aortocoronary bypass graft due to the aortotomy being larger than the vein graft diameter. This results in the wall of the vein being under tension, so that the anastomotic suture or further stitches may cut through. A partial thickness suture placed as a pursestring around the aortotomy may alleviate this situation, resulting in a smaller aortotomy with reduced vein wall tension, improved hemostasis, and a more satisfactory anastomotic vein contour.