Wavelet-based image compression algorithms have good performance and produce a rate scalable bitstream that can be decoded efficiently at several bit rates. Unfortunately, the discrete wavelet transform (DWT) has relatively high computational complexity. On the other hand, the discrete cosine transform (DCT) has low complexity and excellent compaction properties. Unfortunately, it is non-local, which necessitates implementing it as a block-based transform leading to the well-known blocking artifacts at the edges of the DCT blocks. This paper proposes a very fast and rate scalable algorithm that exploits the low complexity of DCT and the low complexity of the set partitioning technique used by the wavelet-based algorithms. Like JPEG, the proposed algorithm first transforms the image using block-based DCT. Then, it rearranges the DCT coefficients into a wavelet-like structure. Finally, the rearranged image is coded using a modified version of the SPECK algorithm, which is one of the best well-known wavelet-based algorithms. The modified SPECK consumes slightly less computer memory, has slightly lower complexity and slightly better performance than the original SPECK. The experimental results demonstrated that the proposed algorithm has competitive performance and high processing speed. Consequently, it has the best performance to complexity ratio among all the current rate scalable algorithms.