When a tumor or other heterogeneous cell population is acutely exposed to ionizing radiation (or, for that matter, to chemotherapeutic agents or hyperthermia), cells that happen to be more sensitive will be preferentially removed, leaving behind a population more resistant as a whole. However, under broadly applicable assumptions, we here demonstrate mathematically that there is a natural tendency of the postirradiation population to recover from the irradiation in such a manner as to restore its original sensitivity composition, i.e. to undergo "resensitization". An important consequence in radiotherapy is that, if a fixed total radiation dose is delivered in a more protracted manner, e.g. as several fractions or as a continuous dose at low dose rate, resensitization occurring over the course of dose delivery will result in greater cell killing than would otherwise have occurred. That is, for a cell population with any form of diversity in radiosensitivity, the influence of redistribution is to make any prolonged dose more damaging than an acute dose of the same magnitude. This tendency toward an "inverse dose-rate effect" may be masked in practice by countervailing effects, such as repair of sublethal damage, but the tendency is demonstrated to hold under very general circumstances, being a consequence of cell-cell diversity and the dynamic response of the cell population to treatment.