[Haskell-cafe] Codensity improvement of free monads

Hello haskell-cafe, I have just read "Asymptotic Improvement of Computations over Free Monads" by Janis Voigtlander, since I have been working with free monads a lot recently and don't want to get hit by their quadratic performance when I start to care about that. But after reading the paper, I still don't really understand how "improve" actually improves anything. Can anyone provide a good explanation for where the work is saved? Luke