Work involving the selection and burn stability control of near-ignited operating points f or the International Thermonuclear Experimental Reactor (ITER) is described. Using simple volume-averaged zero-dimensional transport models, it is suggested that ITER operation at high densities (1 to 2 × 1020/m3) and low temperatures (6 to 10 keV) may be necessary, or even desirable, even though these plasma parameters are intrinsically thermally unstable. It is argued that these thermal instabilities can be effectively controlled using active feedback based on standard diagnostic signals. In particular, the physical and technological feasibility of three control methods, modulation of neutral beam power, modulation of fueling rate, and controlled injection of impurities, is considered, and recommendations regarding the applicability of these methods to ITER are made.