Jane Quilter, I insert a pin straight down through the intersection of both halves, and put a tiny dot of glue on each side of the pin in the seam allowance. For me, it's the best way to match the points.
Watson, it is not paper pieced; the wedges are strip pieced.
Thank you again, everyone, for the comments. I've decided to go with this new thread in the blocks, and probably will use the first one in the border. Both are variegateds, BTW. You probably won't hear from me again for awhile!
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Daffy