A concurrent system behaves fairly if any event that retains a chance to happen will actually happen. “Fairness” is the (younger and less prominent) brother of “liveness” in the family of notions discussed in Petri net literature. Under a closer look, “fairness” resolves into an infinite hierarchy of “k-fairnesses”; the paper discusses this hierarchy. It is shown that for extended simple Petri nets (hence, for semaphore control structures in Dijkstra’s sense [1]), the whole hierarchy collapses into a unique notion.