Any reason you won't consider applique? Round is one of the easiest shapes to do applique (machine or hand). Cut a circle out of heat resistant template plastic or cardboard the size circle you want. Cut your fabric 1/2" (or more) bigger in diameter. Do a very loose basting stitch around the outer edge of your fabric circle, leaving very long tails on the thread. Place template over fabric (wrong side up) and draw your basting threads tight around the template forming a perfect circle. Flip it over press well, remove your template. Ta-dah you have a beautiful perfect circle you can now stitch down to your background fabric. I did this entire quilt that way. And my circles in this quilt were 5" appliqued on to 6" squares. [ATTACH=CONFIG]393233[/ATTACH]