This article presents four modifications to the JPEG arithmetic coding (JAC) algorithm, a topic not studied well before. It then compares the compression performance of the modified JPEG with JPEG XR, the latest block-based image coding standard. We first show that the bulk of inter/intra-block redundancy, caused due to the use of the block-based approach by JPEG, can be captured by applying efficient prediction coding. We propose the following modifications to JAC to take advantages of our prediction approach. 1) We code a totally different DC difference. 2) JAC tests a DCT coefficient by considering its bits in the increasing order of significance for coding the most significant bit position. It causes plenty of redundancy because JAC always begins with the zeroth bit. We modify this coding order and propose alternations to the JPEG coding procedures. 3) We predict the sign of significant DCT coefficients, a problem is not addressed from the perspective of the JPEG decoder before. 4) We reduce the number of binary tests that JAC codes to mark end-of-block. We provide experimental results for two sets of eight-bit gray images. The first set consists of nine classical test images mostly of size 512 × 512 pixels. The second set consists of 13 images of size 2000 × 3000 pixels or more. Our modifications to JAC obtain extra-ordinary amount of code reduction without adding any kind of losses. More specifically, when we quantize the images using the default quantizers, our modifications reduce the total JAC code size of the images of these two sets by about 8.9 and 10.6%, and the JPEG Huffman code size by about 16.3 and 23.4%, respectively, on the average. Gains are even higher for coarsely quantized images. Finally, we compare the modified JAC with two settings of JPEG XR, one with no block overlapping and the other with the default transform (we denote them by JXR0 and JXR1, respectively). Our results show- that for the finest quality rate image coding, the modified JAC compresses the large set images by about 5.8% more than JXR1 and by 6.7% more than JXR0, on the average. We provide some rate-distortion plots on lossy coding, which show that the modified JAC distinctly outperforms JXR0, but JXR1 beats us by about a similar margin.