I starch the material, baste it to the stabiliser (and hope for the best) - and it usually works out well.

I always use cut away medium weight stablizer I tried the iron on stablizer, did't work.

You could try fusing Fusible No Show Mesh onto the back of the fabric before doing the embroidery.
It is light weight and will not change the drape of the fabric and will not add bulk to the fabric or design that you stitch on the blocks.
It is a cut away stabilizer but you can leave it on the back of the blocks because is is so light weight and just go ahead and stitch your blocks together.

EastWitch2

dailylaundry thanks for asking this question there is so much useful information from everyone in their answers

You have some great advice - glad you took the chance to ask the question. *4U

The Fusbile mesh is one idea. Too, it may be that you need 2 layers of the cutaway stabilizer to keep it from puckering. I have found that some of the designs are pretty dense for a quilt block, and the double layers work better. I was reading about quilt blocks with embroidery not too long ago, and whoever was writing the article recommended that.

Have taken to washing and drying not only the fabric but the batting also. If it looks bad before you wash it then after washing and drying (I usually line dry mine) will make it pucker more. The other hints are all good.

there is a new product out called BATALIZER is is specifically used for quilting. check quilt stores or there is a source online I believe at a site called hoop sisters. they have some amazing embroidery there and amazing patterns