In designing a routing scheme for a communication network it is desirable to use as short as possible paths for routing messages, while keeping the routing information stored in the processors' local memory as succinct as possible. The efficiency of a routing scheme is measured in terms of its stretch factor-the maximum ratio between the cost of a route computed by the scheme and that of a cheapest path connecting the same pair of vertices. This paper presents several simple families of routing schemes for general networks, featuring some desirable properties. Our two main families are the hierarchical covering pivots schemes HCPk and the hierarchical balanced schemes HBk (for k ≥ 1). The scheme HCPk guarantees a stretch factor of 2k - 1 and requires storing a total of O(k · n1 + 1 klog2 n) bits of routing information in the network. The new important features of these schemes are applicability to networks with arbitrary edge costs and attractive stretch factors for small values of k. The purpose of the second method is to provide balanced bounds on the memory requirements of the individual vertices. The scheme HBk guarantees a stretch factor of 2 · 3k - 1 and requires storing at most O(k log n(d + n 1 k)) bits of routing information in a vertex of degree d and O(kn1 + 1 klog n) bits overall. We also describe an efficient distributed preprocessing algorithm for this scheme, which requires same amount of space. © 1990.