We propose routing schemes that optimize the average number of hops for lookup requests in Peer-to-Peer (P2P) systems without adding any overhead to the system. Our work is inspired by the recently introduced variation of greedy routing, called neighbor-of-neighbor (NoN), which allows to get optimal average path length with respect to the degree. Our proposal has the advantage of first "limiting" and then "eliminating" the use of randomization. As a consequence, the NoN technique can be implemented with our schemes without adding any overhead. Analyzed networks include several popular topologies: Chord, Hypercube based networks, Symphony, Skip-Graphs. Theoretical results and extensive simulations show that the proposed simplifications (while maintaining the original node degree) do not increase the average path length of the networks, which is often improved in practice. The improvement is obtained with no harm to the operational efficiency (e.g. stability, ease of programming, scalability, fault-tolerance) of the considered systems.