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Earlier investigations with BGO positron emission tomography (PET) scanners showed that the scatter correction technique based on multiple acquisitions with different energy windows are problematic to implement because of the poor energy resolution of BGO (22%), particularly for whole-body studies. The authors believe that these methods are likely to work better with NaI(Tl) because of the better energy resolution achievable with NaI(Tl) detectors (10%). Therefore, they investigate two different choices for the energy window, a low-energy window (LEW) on the Compton spectrum at 400-450 keV, and a high-energy window (HEW) within the photopeak (lower threshold above 511 keV). The results obtained for the authors' three-dimensional (3-D) (septa-less) whole-body scanners [axial field of view (FOV) of 12.8 cm and 25.6 cm] as well as for our 3-D brain scanner (axial FOV of 25.6 cm) show an accurate prediction of the scatter distribution for the estimation of trues method (ETM) using a HEW, leading to a significant reduction of the scatter contamination. The dual-energy window (DEW) technique using a LEW is shown to be intrinsically wrong; in particular, it fails for line source and bar phantom measurements. However, the method is able to produce good results for homogeneous activity distributions. Both methods are easy to implement, are fast, have a low noise propagation, and will be applicable to other PET scanners with good energy resolution and stability, such as hybrid NaI(Tl) PET/SPECT dual-head cameras and future PET cameras with GSO or LSO scintillators.