The dual-energy window Compton-scattering correction technique is defined here especially for accurate quantification of focal regions having higher than average uptake. The quantification is relative to a known-activity reference source. The scatter multiplier ("k" value) is determined for a radioactive 99mTc sphere on or off the axis of a cylinder containing water with or without background. Both maximum likelihood and filtered-backprojection reconstruction are employed. Either projections or tomograms are corrected. With tight regions of interest, there is a tendency for the requisite "k" value to be slightly lower as the diameter of the cylinder is increased. Neither sphere location nor background perturbs "k", however, so a constant value is a good, first approximation. Then a two-sphere validation test yields an accuracy of 8% with subtracted-tomograms ("k" = 1.30) and 2% with subtracted-projections ("k" = 1.20). With a reference-source region of interest which is four times larger, "k" is reduced and also now depends on background. Although equivalent quantitatively, maximum likelihood is preferable to filtered backprojection with Chang attenuation correction since it produces a less-noisy image.