A technique called 'ballistic damping' is proposed for the control of ion cyclotron instabilities of the highly coherent type characteristically observed in mirror-confined plasmas at high plasma density. Ion beams, launched parallel to the field lines, transit the plasma resonantly gaining perpendicular energy from the unstable wave. These ions exit through the far mirror, thereby extracting energy from the wave. Critical beam currents required to achieve marginal stability, as estimated from power balance considerations, lie well within existing beam technology, both for present mirror or tandem mirror experiments and for scaled-up systems.