An alternate formulation of the microdosimetric-kinetic (MK) model is presented that applies to irradiation of mammalian cells with ultrasoft X rays as well as high-energy radiations of variable linear energy transfer (LET). Survival and DNA double-strand break measurements for V79 cells from the literature are examined to illustrate application of the model. It is demonstrated that the linear component of the linear-quadratic survival relationship (alpha) is enhanced because repairable potentially lethal lesions formed from a single ultrasoft X-ray energy deposition event, when closer on average than for a single high-energy radiation event, are more likely to combine to form a lethal lesion. The quadratic component (beta) of the linear-quadratic survival relationship is increased because the potentially lethal lesions formed by ultrasoft X rays are created with greater efficiency than those of high-energy radiation. In addition, potentially lethal lesions from very low-energy carbon K-shell X rays may be enriched in structural forms that favor combination to form lethal lesions instead of repair. These features account for the increased effectiveness of killing of V79 cells by ultrasoft X rays compared to cobalt-60 gamma radiation. The importance of pairwise combination of potentially lethal lesions to form exchange chromosome aberrations that become lethal lesions is discussed. The extended MK model explains and reconciles differences between the MK model and the theory of dual radiation action on the one hand, and on the other, the view that variation in the RBE with radiation quality is explained by differences in energy deposition in nanometer- rather than micrometer-size volumes.