I ended up writing to Becky of 'Piece O' Cake', because it was her book I learned applique from. She was so nice, and answered right away. I sent her close-up photos of the pucker problem, and she suggested I make sure to smooth out the background on the back before I took that first stitch on the second side of the point. I tried that on my current applique project, and no puckers! The puckers are not too obvious on this piece, and I don't think they will be an issue once it is quilted.
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