Using Fusible Web on Appliques can make them stiff so I found that if I apply the Fusible Web to the Applique & then pull the webbing and fabric apart in the center, I could snip a hole into the webbing and trim the webbing away from the center. By doing this I was left with only a thin strip of fusible webbing around the edge of the applique no more than a 1/4". I could then iron the applique in place and stitch it into place. The only part of the applique that has any stiffness to it is the outer most edge and not very noticable because of the stitching that is in place. I find this works wonders on all my applique projects. Hope this helps.
