We have redeveloped a high-energy x-ray spectra estimation method reported by Iwasaki et al. [A. Iwasaki, H. Matsutani, M. Kubota, A. Fujimori, K. Suzaki, and Y. Abe, Radiat. Phys. Chem. 67, 81-91 (2003)]. The method is based on the iterative perturbation principle to minimize differences between measured and calculated transmission curves, originally proposed by Waggener et al. [R. G. Waggener, M. M. Blough, J. A. Terry, D. Chen, N. E. Lee, S. Zhang, and W. D. McDavid, Med. Phys. 26, 1269-1278 (1999)]. The method can estimate spectra applicable for media at least from water to lead using only about ten energy bins. Estimating spectra of 4-15 MV x-ray beams from a linear accelerator, we describe characteristic features of the method with regard to parameters including the prespectrum, number of transmission measurements, number of energy bins, energy bin widths, and artifactual bipeaked spectrum production.