To review the relative importance of the single-hit mechanism of radiation killing for tumour response to 1.8-2.0 Gy day −1 fractions and to low dose-rate brachytherapy. Tumour cell killing by ionizing radiation is well described by the linear-quadratic equation that contains two independent components distinguished by dose kinetics. Analyses of tumour cell survival curves that contain six or more dose points usually provide good estimates of the α- and β-inactivation coefficients. Superior estimates of tumour cell intrinsic radiosensitivity are obtained when synchronized populations are employed. The characteristics of single-hit inactivation of tumour cells are reviewed and compared with the characteristics of β-inactivation. Potential molecular targets associated with single-hit inactivation are discussed along with strategies for potentiating cell killing by this mechanism. The single-hit mechanism of tumour cell killing shows no dependence on dose-rate and, consequently, no evidence of sublethal damage repair. It is uniquely potentiated by high linear-energy-transfer radiation, exhibits a smaller oxygen enhancement ratio and exhibits a larger indirect effect by hydroxyl radicals than the β-mechanism. α-inactivation coefficients vary slightly throughout interphase but mitotic cells exhibit extremely high α-coefficients in the range of those observed for lymphocytes and some repair-deficient cells. Evidence is accumulating to suggest that chromatin in compacted form could be a radiation-hypersensitive target associated with single-hit radiation killing. Analyses of tumour cell survival curves demonstrate that it is the single-hit mechanism (α) that determines the majority of cell killing after doses of 2Gy and that this mechanism is highly variable between tumour cell lines. The characteristics of single-hit inactivation are qualitatively and quantitatively distinct from those of β-inactivation. Compacted chromatin in tumour cells should be further investigated as a radiation-hypersensitive target that could be modulated for therapeutic advantage.