The execution order of the main components in a JPEG2000 encoder, i.e. the coding sequence, plays a significant role in its performance, implementation cost and memory requirement. The coding sequence is mainly affected by the bit allocation strategy. Existing strategies either require a large working memory or can not be used in rate constrained applications. In this paper, an improved pre-compression bit allocation algorithm for rate-constrained applications of JPEG2000 is proposed. Using the proposed method with multi-layered coding, the memory requirement of a JPEG2000 system is reduced by more than 80%. This is at the expense of a quality degradation of merely 0.47 dB in average, for higher compression ratios of 50 to 100.