A highly successful approach to route planning in networks (particularly road networks) is to identify a hierarchy in the network that allows faster queries after some preprocessing that basically inserts additional "shortcut"-edges into a graph. In the past there has been a succession of techniques that infer a more and more fine grained hierarchy enabling increasingly more efficient queries. This appeared to culminate in contraction hierarchies that assign one hierarchy level to each vertex. In this paper we show how to identify an even more fine grained hierarchy that assigns one level to each edge of the network. Our findings indicate that this can lead to considerably smaller search spaces in terms of visited edges. Currently, this rarely implies improved query times so that it remains an open question whether edge hierarchies can lead to consistently improved performance. However, we believe that the technique as such is a noteworthy enrichment of the portfolio of available techniques that might prove useful in the future.