In many practical scenarios, image encryption has to be conducted prior to image compression. This has led to the problem of how to design a pair of encryption and compression algorithms such that compressing the encrypted image can still be efficiently performed. In this work, we propose a permutation-based image encryption method conducted over the prediction error domain. We also design an arithmetic coding (AC)-based approach to efficiently compress the encrypted image. It can be shown that the proposed scheme can provide reasonably high level of security. More notably, the compression performance on the encrypted image is only slightly degraded, compared with that of compressing the original, un-encrypted one. In contrast, most of the existing approaches induce significant penalty on the compression performance.