High-resolution beams of low-energy (20-2000 eV) electrons are obviously attractive because of the very compact volume of interaction between the beam and sample, and because the associated high secondary emission coefficient minimizes charging of insulating samples. Previous work showed that values of aberration coefficients can be scaled down with voltage and minimum values are achieved by maximizing the focusing field. Here we derive some very simple expressions for the minimum beam diameter and show some experimental results. For a magnetic lens with a constant field of 1 T operating at a large demagnification, the limiting beam diameter is set by chromatic aberration (with an energy spread of 1 eV) and diffraction, and is approximately d(m) = 126 V-1/2 nm, where V is the electron energy in eV; the dependence on magnetic field strength B is B-1/2. For a retarding field lens operating at a large demagnification and with the final landing voltage V much less than the accelerating potential, the limiting value of beam diameter is given by d(e) = 17 V-1/4 nm; the dependence on electric field strength E is E-1/2 . Experimentally, preliminary results were obtained with a small, (permanent) magnetic lens that approximates the constant field case and can be inserted into the work chamber of a conventional scanning electron microscope (SEM). This added immersion lens effectively extends the range of operation of an ordinary SEM down to low energy, and has so far achieved 40 nm resolution at 300 V.