JPEG XS is a new standard for low-latency and low-complexity coding designed by the JPEG committee. Unlike former developments, optimal rate distortion performance is only a secondary goal; the focus of JPEG~XS is to enable cost-efficient, easy to parallelize implementations suitable for FPGAs or GPUs. In this article, we shed some light on the entropy coding back-end of JPEG~XS and introduce modifications of the entropy coding stage currently under discussion that improve objective and subjective quality of the compressed images without compromising the parallelism of the original algorithm.