After I saw this happen a few times, I stopped taking the time to carefully place my trash, and just held onto it until I found an emptier receptacle. After all, emptying public trashcans is already a terrible job. The garbageman isn't carrying a broom and dustpan. Why make his job more difficult?

(I would distinguish public trashcans like this from e.g. commercial trashcans for the use of customers of private businesses. First, they should never fill over halfway. Second, the whole thing should be kept clean. Anything else is a failure of management.)