In this paper, a precompression quality-control algorithm is proposed. It can greatly reduce computational power of the embedded block coding (EBC) and memory requirement to buffer bit streams. By using the propagation property and the randomness property of the EBC algorithm, rate and distortion of coding passes is approximately predicted. Thus, the truncation points are chosen before actual coding by the entropy coder. Therefore, the computational power, which is measured with the number of contexts to be processed, is greatly reduced since most of the computations are skipped. The memory requirement, which is measured with the amount required to buffer bit streams, is also reduced since the skipped contexts do not generate bit streams. Experimental results show that the proposed algorithm reduces the computational power of the EBC by 80% on average at 0.8 bpp compared with the conventional postcompression rate-distortion optimization algorithm. Moreover, the memory requirement is also reduced by 90%. The average PSNR degrades only about 0.1-0.3 dB, on average.