  Space charge effects play significant role in modern-day accelerators. These
effects frequently constrain attainable beam parameters in an accelerator - or
- in an accelerator chain. They also could limit the luminosity of hadron
colliders operating either at low energies or with a sub-TeV high brightness
hadron beams. A number of schemes for compensating space charge effects in a
coasting (e.g. continuous) hadron beam were proposed and some of them had been
tested. But all of these methods do not address the issue of tune spread
compensation of a bunched hadron beam, e.g. the tune shift dependence on the
longitudinal position inside the bunch. In this paper we propose and evaluate a
novel idea of using a co-propagating electron bunch with miss-matched
longitudinal velocity to compensate the space charge induced tune-shift and
tune spread. We present a number of practical examples of such system.
