Reversible data hiding in compressed images is a technique to carry secret data in an image of compressed domain, and is able to restore the original compressed codes from the embedded ones. In 2018, Chang et al. proposed a low-bitrate reversible data hiding method for AMBTC compressed images. Their method uses joint neighborhood coding (JNC)technique for data embedment. The binary representation of quantized value and its prediction result are xor-ed to generate the prediction error and thus, the sign bit can be eliminated. However, their method does not fully consider the neighboring pixels' correlation, and the use of xor-ed prediction errors may cause inaccurate prediction. We propose a new method to improve Chang et al.'s work by better consider the neighboring correlations. Instead of the binary code, we use the Gray code, in which the two successive decimal values differ in only one bit, to obtain the xor-ed prediction errors. Moreover, the indicators are redesigned to better classify the encoding cases. The experimental results indicate that our method offers a lower bitrate when comparing with Chang et al.'s and some recently published works.