Alpha-particle emitters are currently being considered for the treatment of micrometastatic disease. Based on in vitro studies, it has been speculated that only a few alpha-particle hits to the cell nucleus are considered lethal. However, such estimates do not consider the stochastic variations in the number of alpha-particle hits, energy deposited, or in the cell survival process itself. Using a tumour control probability (TCP) model for alpha-particle emitters, we derive an estimate of the average number of hits to the cell nucleus required to provide a high probability of eradicating a tumour cell population. In simulation studies, our results demonstrate that the average number of hits required to achieve a 90% TCP for 10 4 clonogenic cells ranges from 18 to 108. Those cells that have large cell nuclei, high radiosensitivities and alpha-particle emissions occurring primarily in the nuclei tended to require more hits. As the clinical implementation of alpha-particle emitters is considered, this type of analysis may be useful in interpreting clinical results and in designing treatment strategies to achieve a favourable therapeutic outcome.