A heavy-particle treatment system exposes a patients treatment volume, during the course of a single treatment session, to beams of heavy particles from a variety of different angles. The source of heavy particles may rotate about the patient to facilitate that variety of different angles. The foregoing can occur pursuant to a treatment plan that accounts for a penetration range as corresponds to the beams of heavy particles and for using at least one lateral beam controlling device to control at least one of the beams of heavy particles.