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