This document discusses SBB(k)-trees, a type of binary search tree that maintains an optimal balance through the use of "pseudo-nodes". It introduces SBB(k)-trees and defines their properties, including that the pseudo-root has height ≤ k+1 and other pseudo-nodes have height between k and k+1. The document then examines maintenance algorithms for operations like insertion and deletion and analyzes the restructuring work involved. It shows that by setting k = O(log log n), SBB(k)-trees can achieve a height of O(log n). Finally, it proposes maintaining two synchronized SBB(k)-trees to hide rebalancing work.