Order-preserving encryption using the hypergeomatric probability distribution leaks about the half bits of a plaintext and the distance between two arbitrary plaintexts. To solve these problems, Popa et al. proposed a mutable order-preserving encoding. This is a keyless encoding scheme that adopts an order-preserving index locating the corresponding ciphertext via tree-based data structures. Unfortunately, it has the following shortcomings. First, the frequency of the ciphertexts reveals that of the plaintexts. Second, the indices are highly correlated to the corresponding plaintexts. For these reasons, statistical cryptanalysis may identify the encrypted fields using public information. To overcome these limitations, we propose a multi-tree approach to the mutable order-preserving encoding. The cost of interactions increases by the increased number of trees, but the proposed scheme mitigates the distribution leakage of plaintexts and also reduces the problematic correlation to plaintexts.