JPEG 2000's most computationally expensive building block is the Embedded Block Coder with Optimized Truncation (EBCOT). This paper evaluates how encoders targeting a parallel architecture such as a GPU can increase their throughput in use cases where very high data rates are used. The compression efficiency in the less significant bit-planes is then often poor and it is beneficial to enable the Selective Arithmetic Coding Bypass style (fast mode) in order to trade a small loss in compression efficiency for a reduction of the computational complexity. More importantly, this style exposes a more finely grained parallelism that can be exploited to execute the raw coding passes, including bit-stuffing, in a sample-parallel fashion. For a latency-or memory critical application that encodes one frame at a time, EBCOT's tier-1 is sped up between 1.1x and 2.4x compared to an optimized GPU-based implementation. When a low GPU occupancy has already been addressed by encoding multiple frames in parallel, the throughput can still be improved by 5% for high-entropy images and 27% for low-entropy images. Best results are obtained when enabling the fast mode after the fourth significant bit-plane. For most of the test images the compression rate is within 1% of the original.