Recently, reversible data hiding in encrypted compressed images (RDHECI) has attracted more attention due to privacy information protection concerns. Meanwhile, AMBTC as one technique of lossy image compression that has lower storage costs and the simplicity in computation and is extensively used in many applications. Hence, this paper proposes an RDHECI scheme based on AMBTC, named O-AMBTC, to address privacy concerns. First, the original image is scrambled in a block-wise manner to generate the scrambled image which then is compressed by an AMBTC compression technique. Subsequently, the derived AMBTC compression codes are encrypted by using the methods of value modulation and stream cipher while the correlations between two quantization levels of AMBTC compression codes are retained and exploited to vacate redundant room to embed secret messages. Data hiding is then performed with the use of PBTL labeling strategy. In addition, another modified AMBTC compression code based RDHECI scheme, called M-AMBTC, is suggested to increase the ability to carry secret messages. In our dual approach, both the AMBTC-compressed image and the secret messages can be correctly recovered. Experimental results show that two proposed schemes are able to achieve average embedding rates as large as 0.6 bpp and 0.8 bpp when the block size is set to 2 × 2, respectively.