Compound cone mounting

In this case you tie part of the fly on the small inner tube. Cut the large outer tube at an angle, slip the inner tube into the outer, and tie the wing and hackle right over the transition point. Finish the fly on the thin tube and slip a cone on when done. Trim the thin tube and melt a collar to keep the cone in place. You can glue both the inner tube and the cone if you want.
You can choose to let the inner tube go all the way through the outer with a collar in each end or just have it go partly through the outer tube.