Recent advances in accelerator technology make possible the attainment of very-high-intensity beams of protons at energies well above the pion-production threshold. It appears that both circular and linear machines will be useful for this purpose. The latter promise beams of ≥ 1 mA under well-controlled conditions. Such proton beams are adequate for providing pure high-intensity beams of negative pions for radiation therapy, under conditions of favorable geometry and of variable size and energy distribution. With π− beams, it is feasible to deposit, at essentially any depth in the human organism, at least 100 rad/min of high-linear-energy transfer radiation. This is quite sufficient for radiation therapy on deep-seated tumors and is accomplished under more favorable conditions than attainable with other radiation sources.