This paper proposes a separable reversible data-hiding scheme in encrypted image which offers high payload and error-free data extraction. The cover image is partitioned into nonoverlapping blocks and multigranularity encryption is applied to obtain the encrypted image. The data hider preprocesses the encrypted image and randomly selects two basic pixels in each block to estimate the block smoothness and indicate peak points. Additional data are embedded into blocks in the sorted order of block smoothness by using local histogram shifting under the guidance of the peak points. At the receiver side, image decryption and data extraction are separable and can be free to choose. Compared to previous approaches, the proposed method is simpler in calculation while offering better performance: larger payload, better embedding quality, and error-free data extraction, as well as image recovery.