The PHase-Aware pRojection Model (PHARM) feature set, built as phase-aware histograms of quantized projections obtained by convolving residuals with random matrices, achieves competitive detection performance against modern adaptive JPEG steganography while having significant computational cost. In this paper, we propose three improvements to the original PHARM, making it more efficient and effective. First, we reduce the maximum projection matrix size to decrease the computational complexity of convolution and better capture steganographic embedding changes. Second, we select more than one phase pair per projection to compute phase-aware histograms, thus correspondingly reducing the number of projections for each residual. Third, the transposition symmetry is also taken into consideration to make our features more robust while preserving the feature dimensionality. The numerous experiments are given to demonstrate the efficiency and effectiveness of our improved PHARM.