Hoop sleeve for hand quilting near the edge
Use a piece of pre-quilted fabric (bought or make your own), so that the part of the sleeve caught in the hoop is approximately the same thickness as your projects.
To make a pattern, trace the outside of the inner hoop on a piece of paper, approximately 1/3 the way around. Draw a straight line from one edge of the curve to the other. Add 1/4" to the curved edge. Cut two pieces of pre-quilted fabric by this pattern.
Measure the depth of the hoop (usually around an inch). Cut a strip of pre-quilted fabric this wide, plus 1/2" (for two 1/4" seams) and the length of the curved edge of the pattern.
Sew a 2- or 3-inch piece of velcro to the wrong side of each semi-circle, positioned so that they match when the pieces are together. These will help keep the sleeve in position on your hoop.
Use the strip to join the two curved pieces together, sewing with 1/4" seams. Optional: topstitch the seams open (this makes the sleeve fit more smoothly, but is a little tricky to do--some of my friends left off this step and their sleeves were fine).
Bind the raw edges using a single thickness of matching fabric or muslin.