Nowadays spectral attenuation measurements on optical fibers are performed using high precision, com mercially available measurement equipment and the cut-back technique. Most instruments use a combination of halogen lamp and monochromator and operate with spectral widths of 5-10 nm. Since the spectral width of the absorption peaks of Si-O-H bonds in standard silica fibers is of the same order of magnitude, a significant error is introduced into these measurements. Our simulation show considerable distortion of the measured data. Basically the measured curve is a convolution of the true attenuation curve and the source spectral distribution. When measured curves are to be interpreted we have to deal with the inverse problem, the deconvolution of the respective curves. We have developed an algorithm to compute the true attenuation values from the measured data by numerically deconvoluting the measured curve with the source spectrum. It is shown, how the mathematical problem can be reduced to solving a system of linear equations. The algorithm is very unstable with respect to measurement errors, as a Monte-Carlo-Simulation shows. The necessary stability for practical purposes is achieved by fitting the data with a smooth function prior to the deconvolution. Finally we derive a procedure to deal with practical curves: The measured data are first fitted with a special set of Gauss-functions describing the OH-absorption peak at 1.4 pm.Then we carry out the numerical deconvolution with the source spectrum and repeat the curve-fit performed earlier. By comparing the two fits and their parameter values we discuss the influence of the spectral width.