Originally Posted by Prism99

The best thing to do is block them. Sharon Schamber has great videos on Youtube that demonstrate how she blocks. One shows how to stretch out a too-small block, while another shows how to shrink a wavy block. Here is a link to one of them. Sorry, I don't remember which video this is. If it's not the one you need, look for another one by her on YouTube.

http://www.youtube.com/watch?v=v-3RIWhBvcA

I know Sharon says to use a hard pressboard (she has another video on how to make one of those) but, for the type of applique you have, I think I would use a towel underneath when blocking so the satin stitching has something to sink into.

When I do satin stitch applique like yours, I don't use a stabilizer at all. I starch the background fabric very heavily instead. Before cutting the background fabric, I mix a 1:1 solution of liquid Sta-Flo starch and water. I put the fabric on my kitchen island and "paint" the fabric with this solution using a large wall painting brush. I throw the saturated fabric in the dryer, then steam iron. The fabric comes out nice and stiff and will keep its shape through all kinds of handling. I have had no tunnelling with satin stitch using this method. I always wash my quilts when they are finished and, of course, the starch just washes out. HTH!