This paper proposes a Psi-cube network that consists of low-height trees of buses desirable for the coherence directories of multilevel snoopy caches. Since the Psi-cube is organized based on a recurrence of the Hamming codes, it has recursive levels each of bused fat-hypercubes, named psi-cubes. A psi-cube is composed of the clusters that are produced by partitioning the nodes with multiple suits of codewords of a Hamming code. Thus every node is the representative node of a unique cluster, while its other nodes have addresses equal to single-bit or detectable double-bit error words of the node's address. The nodes are connected to a bus in the cluster, so that the Psi-cube configures trees of buses that has the height determined by the recurrence.