If the project piece is large enough, I cut out the center and just leave the fusible about 1/4 inch inside the drawn lines and less than 1/4 inch on the outside. After pressing it to the wrong side of the fabric, I cut it out on the drawn line, then press it to the background, then straight stitch or blanket stitch it in place. It keeps the center softer, but gives stability to the edge for sewing it down.