The JPEG standard was vastly successful. Currently, the first AI-based compression method ``JPEG AI'' will be standardized. JPEG AI brings remarkable benefits. JPEG AI images exhibit impressive image quality at bitrates that are an order of magnitude lower than images compressed with traditional JPEG. However, forensic analysis of JPEG AI has to be completely re-thought: forensic tools for traditional JPEG do not transfer to JPEG AI, and artifacts from JPEG AI are easily confused with artifacts from artificially generated images (``DeepFakes''). This creates a need for novel forensic approaches to detection and distinction of JPEG AI images. In this work, we make a first step towards a forensic JPEG AI toolset. We propose three cues for forensic algorithms for JPEG AI. These algorithms address three forensic questions: first, we show that the JPEG AI preprocessing introduces correlations in the color channels that do not occur in uncompressed images. Second, we show that repeated compression of JPEG AI images leads to diminishing distortion differences. This can be used to detect recompression, in a spirit similar to some classic JPEG forensics methods. Third, we show that the quantization of JPEG AI images in the latent space can be used to distinguish real images with JPEG AI compression from synthetically generated images. The proposed methods are interpretable for a forensic analyst, and we hope that they inspire further research in the forensics of AI-compressed images.