Prism99

It sounds to me as if your background fabric stretched as you were stitching. Since you were stitching all around the appliques, then some of the stitching was on the bias of the background fabric. More stitches piled up on the bias and less on the straight-of-grain, resulting in waves.

I have found that heavily starching the background fabric can substitute for using a stabilizer. By heavy starching, I mean *heavy* starching! I starch before cutting the background squares, using a 1:1 solution of Sta-Flo liquid laundry starch and water. My method is to lay the folded yardage on my kitchen island, then use a large wall-painting brush to apply the solution until the fabric is saturated. Unstarched yardage stays folded to my left, and as I finish a starched section I fold it over to make sure that the other side is saturated to. Makes handling the fabric pretty easy. Once the fabric is saturated, I toss it in the dryer and then iron with steam. The resulting fabric has a stiffness similar to cardstock.

Some people are concerned about starch "dust" getting into their sewing machine works. I have a Bernina 1230 and this has not been a problem for me.

Experiment to see if you need to loosen your satin stitch too. (This means increasing stitch length slightly.) I have not found this to be necessary with the starched background. Another option for loosening the satin stitch is to go around each applique twice, first with a slightly narrower stitch and then again with a slightly wider stitch. Makes for a very full edge. I tried this, but felt it made the edge too stiff for the thread that I usually use, plus it doubled the stitching time!