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I've done embroidered blocks in a few quilts. OESD makes a real thin fusible fleece that I put on the block fabric without any other stabilizer. Sometimes I fuse it to the fabric first but if I don't want to do that I just hoop it like stabilizer then cut it away from the embroidery after I've finished it. It's very thin but it does give just the right stability to cotton fabric. Then I just use my regular batting and backing.
Cari