Since the introduction of JPEG 2000, several rate control methods have been proposed. Among them, post-compression rate-distortion optimization (PCRD-Opt) is the most widely used, and the one recommended by the standard. The approach followed by this method is to first compress the entire image split in code blocks, and subsequently, optimally truncate the set of generated bit streams according to the maximum target bit rate constraint. The literature proposes various strategies on how to estimate ahead of time where a block will get truncated in order to stop the execution prematurely and save time. However, none of them have been defined bearing in mind a parallel implementation. Today, multi-core and many-core architectures are becoming popular for JPEG 2000 codecs implementations. Therefore, in this paper, we analyze how some techniques for efficient rate control can be deployed in GPUs. In order to do that, the design of our GPU-based codec is extended, allowing stopping the process at a given point. This extension also harnesses a higher level of parallelism on the GPU, leading to up to 40% of speedup with 4K test material on a Titan X. In a second step, three selected rate control methods are adapted and implemented in our parallel encoder. A comparison is then carried out, and used to select the best candidate to be deployed in a GPU encoder, which gave an extra 40% of speedup in those situations where it was really employed.