State-of-the-art JPEG steganographic algorithms, such as J-UNIWARD, are currently better detected in the spatial domain rather than the JPEG domain. Rich models built from pixel residuals seem to better capture the impact of embedding than features constructed as co-occurrences of quantized JPEG coefficients. However, when steganalyzing JPEG steganographic algorithms in the spatial domain, the pixels’ statistical properties vary because of the underlying 8 × 8 pixel grid imposed by the compression. In order to detect JPEG steganography more accurately, we split the statistics of noise residuals based on their phase w.r.t. the 8 × 8 grid. Because of the heterogeneity of pixels in a decompressed image, it also makes sense to keep the kernel size of pixel predictors small as larger kernels mix up qualitatively different statistics more, losing thus on the detection power. Based on these observations, we propose a novel feature set called PHase Aware pRojection Model (PHARM) in which residuals obtained using a small number of small-support kernels are represented using first-order statistics of their random projections as in the projection spatial rich model PSRM. The benefit of making the features “phase-aware” is shown experimentally on selected modern JPEG steganographic algorithms with the biggest improvement seen for J-UNIWARD. Additionally, the PHARM feature vector can be computed at a fraction of computational costs of existing projection rich models.