An important aspect of heavy charged particle radiotherapy is its ability to localize dose to the target volume. Current techniques generally employ beam delivery schemes which use range modulated beams in which the Bragg peak is spread out over a range of depths. The range modulation is constant over the entire beam cross section. This paper examines the potential gain from the use of variable range modulation over the beam cross section which can be achieved through beam scanning. An analytic technique has been developed to calculate a gain factor, related to integral dose, for a number of different charged particle beams. The dependence of the gain factor on tumor depth, diameter, and size has been examined. These analytic results have been compared with computer calculations of treatment plans simulating beam scanning and fixed modulation delivery techniques for actual clinical cases. The rationale for beam scanning, and its potential impact on tumor control is discussed.