Applying the space-charge forces of a low-energy electron beam can lead to a significant improvement of the beam-particle lifetime limit arising from the beam–beam interaction in a high-energy collider [1]. In this paper, we present the results of various beam experiments with 'electron lenses', novel instruments developed for the beam–beam compensation at the Tevatron, which collides 980 GeV proton and antiproton beams. We study the dependencies of the particle betatron tunes on the electron beam current, energy and position; we explore the effects of electron-beam imperfections and noises; and we quantify the improvements of the high-energy beam intensity and the collider luminosity lifetime obtained by the action of the Tevatron electron lenses.