We have reviewed applicable ranges for attenuating media and off-axis distances regarding the high-energy X-ray spectra reconstructed via the Iwasaki-Waggener iterative perturbation method for 4-20 MV X-ray beams. Sets of in-air relative transmission data used for reconstruction of spectra were calculated for low- and high-Z attenuators (acrylic and lead, respectively) by use of a functional spectral formula. More accurate sets of spectra could be reconstructed by dividing the off-axis distances of R = 0-20 cm into two series of R = 0-10 cm and R = 10-20 cm, and by taking into account the radiation attenuation and scatter in the buildup cap of the dosimeter. We also incorporated in the reconstructed spectra an adjustment factor (f (adjust) ≈ 1) that is determined by the attenuating medium, the acceleration voltage, and the set of off-axis distances. This resulted in calculated in-air relative transmission data to within ±2 % deviation for the low-Z attenuators water, acrylic, and aluminum (Al) with 0-50 cm thicknesses and R = 0-20 cm; data to within ±3 % deviation were obtained for high-Z attenuators such as iron (Fe), copper (Cu), silver (Ag), tungsten (W), platinum (Pt), gold (Au), lead (Pb), thorium (Th), and uranium (U) having thicknesses of 0-10 cm and R = 0-20 cm. By taking into account the radiation attenuation and scatter in the buildup cap, we could analyze the in-air chamber response along a line perpendicular to the isocenter axis.