This link comes via the fine folks from the Southeast Fly Fishing Forum. Forum user Flytier pointed us to the UK Saltwater Fly Fishing site for this simple method for repairing a nicked or cut fly line using shrink tubing. It seems so easy that it makes me wonder why I didn't think of it myself. Luckily our UK brethren worked it out for the rest of us.
"Some lines are easier to fix than others and I know we had problems trying this with Rio lines due to the core not being able to take the heat. Rio use a slightly stiffer PVC than other manufacturers. We've not tried this on Airflo line because.. well, we don't know anyone who uses Airflo lines."