In this paper, we propose two format-compliant encryption schemes for JPEG2000, which preserve the syntax of the original codestream and do not introduce superfluous markers into the encrypted bitstream. The proposed efficient scheme randomly encrypts either low or upper half bytes of those randomly selected bytes in Codeblock Contribution to Packets (CCPs). The secure scheme encrypts both low and upper half bytes and can protect the nearly whole codestream except for the header information. The proposed schemes can provide efficient, secure, scalable and completely format-compliant protection of JPEG2000, which is proved by lots of experiments.