This paper discusses some aspects of deconvolution of one-dimensional spectra in the framework of the Least Squares Method and presents a minimum variance regularization procedure. Covariance matrices are taken into account inevery step. Fluctuation and artifacts, both in the deconvolved and regularized spectra, are related to the structure of the covariance matrices. The method is applied to a simulated spectrum and to the 34S (gamma, <img src="http:/img/fbpe/bjp/v31n1/02eq05.gif">n) cross section determination from actual yield data.