To support secure database management, a number of value-added encryption schemes have been studied including order-revealing encryption (ORE) schemes. One of outstanding features of ORE schemes is the efficiency of range queries in an encrypted form. Compared to existing encryption methods, ORE leads to an increase in the length of ciphertexts. To improve the efficiency of ORE schemes in terms of the length of ciphertext, a new ORE scheme with shorter ciphertext has been proposed by Kim. In this paper, we revisit Kim's ORE scheme and show that the length of ciphertexts is not as short as analyzed in their paper. We also introduce a simple modification reducing the memory requirement than existing ORE schemes.