In electron guns, three lenses are present: the cathode lens, projecting a crossover in front of it, the main lens that images the crossover on the target, and the prefocusing lens situated in between, adapting the aperture angle to the main lens. The spot size at the target is calculated for different positions and strengths of the prefocusing lens. The analysis is based on a phase space representation of the rotationally symmetric beam. It is shown that by proper choice of the position and strength of the prefocusing lens, the resulting selective prefocusing lens (SPL) reduces the combined spherical aberration of the cathode lens and main lens by 45%. The intensity distributions in the spot with and without the SPL differ greatly and a more uniform spot intensity is obtained.