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A novel compression and encryption scheme using variable model arithmetic coding and coupled chaotic system, different from the traditional way which compresses the data first and then encrypts the compressed bit-stream later, can encrypt and compress the input plaintext synchronously. In this paper, an improved scheme using variable interval arithmetic coding and asymptotic deterministic randomness has been proposed. The improved scheme is secure because the key bit-stream generated by the asymptotic deterministic randomness can resist previous attacks against chaotic encryption. In addition, the compression efficiency will not change with the key bit-stream, because the statistical model will no longer be changed. The results show that the new scheme can achieve high compression efficiency.