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Variable-rate bit streams generated under the current DCT-based JPEG standard are vulnerable to propagation of error across the data units, i.e., DCT blocks. A traditional approach to combat this problem has been to introduce resynchronization markers in the transmitted bitstream. We propose an alternative, and more efficient, approach based on constraining the data length for the blocks or groups of blocks in the compressed image. In the proposed scheme the number of coded bits in each block, or group of blocks, is sent to the decoder as side information and thus the decoder can introduce resynchronization markers. The required overhead is significantly less than that of typical explicit synchronization schemes (e.g., those in JPEG). In addition, it is possible to further constrain the allowable rates for the blocks in order to reduce the overhead. We show experimental results where the constrained rate allocation is performed using thresholding techniques on images encoded by the baseline JPEG.