I also trace the pieces onto Wonder Under (it is cheaper than Steam A Seam) then fuse and cut out. I use batiks because the tighter weaves helps prevent fraying. The bulk of the satin stitch is on the applique and I use 30 wt. thread for a bit smoother stitch. The narrower your stitch the more wobbles will show. The tear away stabilizer that I use is the wall liner used before wallpapering uneven surfaces. You can also satin stitch the "inside" of the applique on the stabilizer, tear away the stabilizer and applique the edges to the background with stabilizer behind it. On large pieces I will protect them with freezer paper ironed on until ready to stitch to the background. The eyes below were stitched separately as was the nose before stitching to the face. (Front and back shot of the eyes, stabilizer removed.)