In efforts to optimize the efficiency of ZK-EVM and BALs, a strategy has been proposed to minimize the overhead associated with intermediate tree nodes. Non-prover nodes can streamline operations by retaining only the leaf nodes, eliminating the need for intermediate nodes entirely. Meanwhile, provers have the option to forego storing the bottom k leaves of the tree, which would necessitate an additional 2^k re-hashing for each read or write operation. This approach, particularly effective with binary trees, can significantly reduce non-leaf storage requirements by a factor of log(n), albeit with a trade-off of increased hashing overhead.