In this study, a new method is proposed to protect JPEG still images through encryption by employing integer-to-integer transforms and frequency domain scrambling in DCT channels. Different from existing methods in the literature, the encrypted image can be further compressed, i.e. transcoded, after the encryption. The method provides selective encryption/security level with the adjustment of its parameters. The encryption method is tested with various images and compared with the methods in the literature in terms of scrambling performance, bandwidth expansion, key size and security. Furthermore this method is applied to the H.263 video sequences for the encryption of I-frames.