It is shown that resolving doublets from high-resolution gamma-ray spectra using spectrum convolution offers several advantages over the usual peak search techniques that work with the original, non-convoluted spectrum. The spectral lines are approximated by Gaussian shapes with known widths and the convolution function is chosen as a projector which eliminates any linear background from the final results. The proposed method is more efficient compared with the standard method in frequently encountered cases where doublets are embedded within other peaks of the spectrum. Analytical expressions for the uncertainties of peak areas are given.