The accuracy of the envelope method, which was proposed by the authors for removing a continuous background from X-ray fluorescence spectra, is studied. This study is performed using model spectra in the presence of different forms of the bremsstrahlung background in the presence of noise in these spectra. For typical conditions, the error is as large as a few tenths of a percent and can be assessed with a suitable accuracy following the algorithm proposed in this paper. It is shown that the envelope method is an efficient technique for removing a continuous bremsstrahlung background from first-order X-ray fluorescence spectra that allow the intensities of spectral lines to be found with a high accuracy without using any data beyond the spectra themselves.