When a cell population in exponential growth is subjected to ionizing radiation, the degree to which its long-term size is attenuated, relative to a control population that is not irradiated, depends not only on the total dose but also on the time pattern of dose delivery. Using a standard mathematical model for cycling cell populations with age-dependent radiosensitivity, it has recently been shown that normal progression of cells through the cycle tends to decrease this relative population size when the total dose delivery time is increased from essentially zero times to short, finite times (Chen et al., Math. Biosci. 126, 147-170, 1995). This mathematical result is an agreement with intuitive arguments and experiments long known in radiobiology. Mechanistically, it says that after the first part of a dose has preferentially eliminated the more sensitive cells of an exponentially cycling cell population, cell cycle progression, with the consequent redistribution of cells among cycle phases, tends to "resensitize" that population, an affect countering that of sublethal damage repair. The present paper now generalizes this result, demonstrating that the redistribution-induced increase of cell killing carries over to doses of arbitrary duration. That is to say, delivering a given dose over some extended period will result in lesser ultimate population size (i.e. population size measured at some fixed time long after irradiation has ceased) than will delivering the same total dose acutely. The redistribution-induced resensitization occurs no matter how radiosensitivity depends on cell age. For illustration, examples are given to show that, for a split dose, the least sensitivity is observed when the two doses coincide. These examples also demonstrate, within the constraints of the overall resensitization principle, the possibility of an oscillatory dependence of population sensitivity on interfraction time.