Terri,
Karen Kay Buckley talked about this in one of her classes. She suggested using a light weight iron on fusible interfacing on the applique shape (not the in seam allowance). Karen mentioned this because a judge commented that one of her quilts had some shadowing. (That must of been years ago...because look at her now!) I tried her idea in a quilt I just finished. I used a white shirting fabric that had many tiny, little black lines and the tiny, little black lines showed through some light colored fabrics, such as yellow. So, here is another suggestion for you think about.