Alpha-particle emitters are currently being evaluated for the treatment of metastatic disease. The dosimetry of alpha-particle emitters is a challenge, however, because the stochastic patterns of energy deposition within cellular targets must be taken into account. We propose a model for the tumor control probability of alpha-particle emitters which takes into account these stochastic effects. An expression for cell survival, which is a function of the microdosimetric single-event specific-energy distribution, is multiplied by the number of cells within the tumor cluster. Poisson statistics is used to model the probability of zero surviving cells within the cluster. Based on this analysis, a number of observations have been made: (1) The dose required to eradicate a tumor is nearly a linear function of the cell survival parameter z(0). (2) Cells with smaller nuclei will require more dose to achieve the same level of tumor control probability, relative to cells with larger nuclei, for an identical source-target configuration and cell sensitivity. (3) As the targeting of alpha-particle emitters becomes more specific, the dose required to achieve a given level of tumor control decreases. (4) Additional secondary effects include cell shape and the initial alpha-particle energy.