If you leave the word "large" out of the equation, a trash compactor bag inside the panniers works for me. I only need the volume of one pannier to stay absolutely dry, so I only use one bag. The trash compactor bag works well because it's white (easier to see into), and it can be patched with duct tape. I also use it as a partial drop cloth when I'm cowboy camping. It's versatile, light, and cheap.