I heavily starch the backing fabric. This stabilizes enough so there are no puckers. My method is to mix a 1:1 solution of Sta-Flo liquid laundry starch and water, "paint" this solution onto yardage using a large wall painting brush, wait a couple of minutes to make sure starch has penetrated the fibers, toss in dryer, then iron with steam. When cutting my background pieces, I cut them an inch bigger just in case there is take-up during the applique process, then cut them to size after sewing; however, this really hasn't been necessary with the heavy starching.
For me, it's easier to starch than to use stabilizer.