In this paper, we present two new methods for efficient rate control and entropy coding in lossy image compression using JPEG-2000. These two methods enable significant improvements in computation complexity and power consumption over the traditional JPEG-2000 algorithms. First, we propose a greedy heap-based rate-control algorithm (GHRaC), which achieves efficient postcompression rate control by implementing a greedy marginal analysis method using the heap sort algorithm. Second, we propose an integrated rate-control and entropy-coding (IREC) algorithm that reduces the computation complexity of entropy coding by selectively entropy coding only the image data that is likely to be included in the final bitstream, as opposed to entropy coding all image data. Together, these two methods enable significant savings in computation time and power consumption. For example, the GHRaC method demonstrates 16 /spl times/ speedup for rate control when encoding the Lena color image using a target compression ratio of 128:1, one quality layer, and code blocks of 32 /spl times/ 32 pixels. The IREC method expands upon GHRaC to perform entropy coding in conjunction with rate control. Using an enhanced version of IREC, these two methods jointly achieve a speedup in execution time of 14 /spl times/ over traditional rate control and entropy coding, which first entropy codes all image coefficients and then separately performs postcompression rate control using the generalized Lagrange multiplier method to select which data are included in the final bitstream. Both theoretical analysis and empirical results are presented in validating the advantages of the proposed methods.