For perfectly round small circles, try this: Draw or trace the desired size circle on a manila file folder.
Cut out the circle. Placing the template on the wrong side of the fabric, trace around it with a pencil.
Cut the patch about 3/16" out from the pencil line.
Hand sew a line of basting stitches midway between the pencil line and the cut edge.
Centering the template within the pencil line, draw up the basting stitches.
Lightly apply spray starch onto the basted seam allowance. Press.
Let cool. Remove the basting stitches and the template.