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Reports on a new numerical implementation of the single-scatter simulation scatter correction algorithm for 3D PET. Its primary advantage over tile original implementation is that it is a much faster calculation, currently requiring less than 30 sec execution time per bed position for an adult thorax, thus making clinical whole-body scatter correction more practical. The new code runs on a single processor workstation CPU instead of a vector processor array, making it highly portable. It is modular and independent of any particular reconstruction code. The computed scatter contribution is now intrinsically scaled relative to the emission image and no longer requires normalization to the scatter tails in the sinogram when all activity is contained within the field of view, making it more robust against noise. The new algorithm has been verified against the original code on both phantom and human thorax studies. Initial results indicate that scatter correction may be accurately performed following, instead of prior to, either 3D reprojection or Fourier rebinning. Some evidence is presented that the single-scatter operator, when applied to an uncorrected emission image provides reasonable compensation for multiple scatter.