Although optimal truncation of JPEG2000 compressed imagery provides an image of the highest quality per bit rate in terms of peak signal to noise ratio, the algorithm is highly computationally inefficient because of the removal of compressed image sections that have been previously calculated. The proposed idea utilizes a simple quantization technique prior to Tier I coding to remove many of the coding passes from the imagery that would not become a part of the final compressed bit stream. Two methods based on the this idea are discussed. The first method restricts the quantization value to be a power of 2, effectively eliminating the least significant bits of each code block through the quantization step. The second method relaxes the 2n restriction. Both methods give substantial reduction in computational complexity, a 39% and 46% reduction in overall complexity at 0.25 bits per pixel, respectively. The first method gives an equivalent rate distortion curve as traditional optimal truncation, and the second gives a similar rate distortion curve, only moderately underperforming traditional optimal truncation in a few images at few bit rates.