The noise penalties of the following resolution-enhancement procedures are compared: (a) deconvolution when the apparatus function is smooth, (b) deconvolution when the apparatus function possesses a step discontinuity, and (c) physically reducing the experimental "slit width" or its equivalent. It is shown that it is not feasible to very significantly increase resolution by deconvolution when the apparatus function is smooth. The method (c) achieves a given resolution increase with the smallest noise increase of these methods. However, method (b) is feasible when the source distribution possesses a discontinuity, and the apparatus resolution is good. This occurs naturally when using a field emission source in electron energy loss spectroscopy. Using the Fermi-level cut-off as a discontinuity in the source distribution, we use method (b) above to obtain deconvoluted data which is limited only by the spectrometer resolution. © 1992.