Try cutting the square to be appliqued on the bias. Bias edges don't fray the way straight-of-grain edges do. Adding a fusible to the square will help also.

Also, on the first block, did you fan the seam allowances at the center? That really helps to flatten the block.

Thanks gals, First block is nicer. I made about 12 of them and there was a problem where all the seams met in the center and corners and even with 'pressing. I decide to fuse light bonding onto center squares and blanket stitch over the edges, it's not as special a treatment of the orginal block has but it's one that I can finish soon as the quilt needs to be delivered next week.

Also, wish I had found out about the 10 minute block a few months ago when I began this quilt, certainly looks very much like my modified block but can be made with a lot less trouble. Thanks again, May in Jersey