Accelerated repopulation (rapid multiplication of surviving clonogens) during a course of radiation therapy may contribute to local failure. This possibility has prompted accelerated treatment programs in an attempt to reduce overall treatment time, thereby minimizing the impact of repopulation. However, accelerated dose delivery at the start of treatment may not be advantageous since many of the tumor cells are likely to be hypoxic (non-cycling cells) and therefore relatively radioresistant. Conversely, accelerated treatment is likely to be most helpful later in treatment when the tumor has shrunk and accelerated repopulation of clonogens is a dominant factor. A series of calculations are presented that stimulate changes in tumor size, clonogen number, clonogen repopulation, and growth fraction during a course of fractionated radiation treatments for an idealized 2 cm diameter spherical tumor. The efficiency of each fraction of radiation is calculated for different radiation fractionation schemes. Efficiency is defined as the change in Log clonogen number (reflecting cell death due to radiation minus repopulation that has occurred during the interval between fractions) per Gy. These calculations suggest that relatively low total daily doses (approximately 2 Gy) are most efficient early in treatment. Higher daily doses are less efficient since the growth fraction is relatively low at the start of treatment. Later in treatment, as the tumor shrinks and the growth fraction approaches 1, accelerated repopulation becomes a major problem and higher total daily doses are more efficient. At this point, accelerated hyperfractionation should be used to increase the daily dose without exposing normal tissues to high fraction sizes. Thus, changes in tumor growth characteristics are exploited and dose delivery can be optimized by escalating daily irradiation doses during a course of fractionated irradiation. Strict interpretation of these conclusions must be tempered by the various assumptions and uncertainties included in this model. The concept of efficiency is useful since it reflects the competing effects of clonogen repopulation and radiation induced clonogen sterilization.