Head-on and long-range induced tunespread of about 0.025 in the Tevatron collider at Run II (together with the increased strength of the resonances) can significantly deteriorate the (bar p) lifetime and the collider luminosity. It was proposed to employ the so-called Tevatron Electron Lenses (TEL) to compress the beam-beam footprint and eliminate completely the bunch-to-bunch tunespread (PACMAN effect) for small amplitude particles. The first lens has been recently installed and tested (1). This report presents results of analytical studies and tracking simulations of the linear beam-beam compensation (elimination of the bunch-to-bunch tune variation). Compression of the beam-beam footprint (nonlinear compensation) is discussed in (2).