When an over-the-cell routing layer is available for standard cell layout, efficient utilization of that routing space over the cells can significantly reduce layout area. In this paper, we present three physical models to utilize the area over the cells for routing in standard cell designs. We also present efficient algorithms to choose and to route a planar subset of nets over the cells so that the resulting channel density is reduced as much as possible. For each of the physical models, we show how to arrange inter-cell routing, over-the-cell routing and power/ground busses to achieve valid routing solutions. Each algorithm exploits the particular arrangement in the corresponding physical model and produces provably good results in polynomial time. We tested our algorithms on two industrial standard cell designs. In these tests, this method reduces total channel density as much as 21%.