The JPEG2000 standard does not specify how to perform the rate control strategy, needed either to achieve a target bitrate, or to construct quality layers. In this paper, an efficient rate control algorithm is described. It is based on the interleaving of coding passes and it has a low computational complexity. The proposed algorithm encodes only the coding passes included in the final codestream, and it fully avoids the need of any post compression rate distortion stage. Extensive experimental results show that the encoding performance of our method is competitive and similar to the optimal strategy. In addition, this proposal allows the extraction of a target bitrate from a codestream without the need of either knowing the original image, or of decoding any part of the codestream. The performance of this kind of extraction is equivalent to that obtained when decompressing a codestream organized in quality layers.