We examine the potential to treat unstable ventilatory control (seen in periodic breathing, Cheyne-Stokes respiration, and central sleep apnea) with carefully controlled dynamic administration of supplementary CO(2), aiming to reduce ventilatory oscillations with minimum increment in mean CO(2). We used a standard mathematical model to explore the consequences of phasic CO(2) administration, with different timing and dosing algorithms. We found an optimal time window within the ventilation cycle (covering approximately 1/6 of the cycle) during which CO(2) delivery reduces ventilatory fluctuations by >95%. Outside that time, therapy is dramatically less effective: indeed, for more than two-thirds of the cycle, therapy increases ventilatory fluctuations >30%. Efficiency of stabilizing ventilation improved when the algorithm gave a graded increase in CO(2) dose (by controlling its duration or concentration) for more severe periodic breathing. Combining gradations of duration and concentration further increased efficiency of therapy by 22%. The (undesirable) increment in mean end-tidal CO(2) caused was 300 times smaller with dynamic therapy than with static therapy, to achieve the same degree of ventilatory stabilization (0.0005 vs. 0.1710 kPa). The increase in average ventilation was also much smaller with dynamic than static therapy (0.005 vs. 2.015 l/min). We conclude that, if administered dynamically, dramatically smaller quantities of CO(2) could be used to reduce periodic breathing, with minimal adverse effects. Algorithms adjusting both duration and concentration in real time would achieve this most efficiently. If developed clinically as a therapy for periodic breathing, this would minimize excess acidosis, hyperventilation, and sympathetic overactivation, compared with static treatment.