There is increasing recognition that treatment failure in cancer may be associated with the failure to sterilize a small subpopulation of tumor cells that have been characterized as tumor stem cells. Defined as cells that are able to self-renew and also to replenish a phenotypically diverse tumor-cell population, such cells are also considered resistant to chemotherapy. These characteristics are optimal for targeting by using alpha-particle-emitting radionuclides. Because of their high-energy deposition density per track, alpha-particles are capable of targeting single cells or small clusters of cells with minimal normal organ toxicity. The DNA damage induced by alpha-particles is largely irreparable and, therefore, alpha-particle-induced damage is minimally susceptible to resistance mechanisms. In this work, theoretical modeling was performed to examine the potential of alpha-emitter targeting of such small clusters of cancer stem cells. Critical parameters influencing efficacy and toxicity were identified and their relationship elucidated. The results identify specific activity, antigen site density, and number of target cells as critical parameters for effective cell killing and demonstrate substantial efficacy gains by targeting a smaller number of stem cells, as opposed to the entire tumor-cell population.