This report examines theoretical and empirical issues related to the statistical power of impact estimates under clustered regression discontinuity (RD) designs. The theory is grounded in the causal inference and HLM modeling literature, and the empirical work focuses on commonly-used designs in education research to test intervention effects on student test scores. The main conclusion is that three to four times larger samples are typically required under RD than experimental clustered designs to produce impacts with the same level of statistical precision. Thus, the viability of using RD designs for new impact evaluations of educational interventions may be limited, and will depend on the point of treatment assignment, the availability of pretests, and key research questions. Appendices include: (1) Values for "Factor(.)" in Equation (1) of Text, by the Number of Degrees of Freedom, for One- and Two-Tailed Tests, and at 80 and 85 Percent Power; and (2) Lemma 1. (Contains 7 tables, 2 figures and 8 footnotes.)