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We present a new overlay, called the {\em Deterministic Decentralized tree}($D^2$-tree). The $D^2$-tree compares favourably to other overlays for thefollowing reasons: (a) it provides matching and better complexities, which aredeterministic for the supported operations; (b) the management of nodes (peers)and elements are completely decoupled from each other; and (c) an efficientdeterministic load-balancing mechanism is presented for the uniformdistribution of elements into nodes, while at the same time probabilisticoptimal bounds are provided for the congestion of operations at the nodes. Theload-balancing scheme of elements into nodes is deterministic and generalenough to be applied to other hierarchical tree-based overlays. Thisload-balancing mechanism is based on an innovative lazy weight-balancingmechanism, which is interesting in its own right.

D$^2$-Tree: A New Overlay with Deterministic Bounds