Two schemes for fast identification of JPEG coded images are proposed in this paper. The aim is to identify the JPEG images that are generated from the same original image and have equivalent or different compression ratios. Fast identification can be achieved since the schemes work on the quantized Discrete Cosine Transform (DCT) domain. It is not required to inverse the quantization and the DCT. Moreover, only a few coefficients are commonly required for identification. The first approach can avoid identification leakage or false negative (FN), and probably result in a few false positives (FP). The second approach can avoid both FN and FP, with a slightly higher processing time. By combining the two schemes, a faster and a more perfect identification can be achieved, in which FN and FP can be avoided.