We define a family of Distributed Hash Table systems whose aim is to combine routing efficiency of the randomized networks - i.e. average path length O(log n/log log n) vs. the O(log n) average path length of the deterministic system - with the programmability and startup efficiency of a uniform system - that is a system in which the overlay network is transitive, and greedy routing is optimal. It is known that \Omega(log n) is a lower bound to the average path length for uniform systems with O(log n) degree. The proposed family is parameterized with a positive integer c which measures the amount of randomness that is used. Indeed, edges are partitioned into c equivalence classes. Varying the value c, the system goes from the deterministic case (c = 1) to an "almost uniform" system. Increasing c to relatively low values allows routing with optimal average path length while retaining most of the advantages of a uniform system, such as easy programmability and quick bootstrap of the nodes entering the system.

We also provide a matching lower bound for the average path length of the family of routing schemes for any c. Moreover, we show how to extend the result to other overlay networks.