In Jax's case, they tell him to quit using weapons.

I think we can officially run with the League asking the champs to tone it down and placing a limiter, and then the champs just finding new ways to make people suffer.

Teemo for example found out he can eat a certain rare root to give himself a burst of energy to run when he is caught scouting.

Also, it's likely that magical champions also may have their powers dampened. For instance, look at Kayle in the RPing event. She was able to use Intervene on everyone at the same time to save their lives. It's very likely that some champions are ages stronger outside of the League.